Defects of properties in mathematics :: quantitative characterizations /
"This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measur...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
©2002.
|
| Schriftenreihe: | Series on concrete and applicable mathematics ;
v. 5. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | "This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--Page 2 of cover. |
| Beschreibung: | 1 online resource (xi, 352 pages) |
| Bibliographie: | Includes bibliographical references (pages 337-348) and index. |
| ISBN: | 9789812777645 9812777644 9789810249243 9810249241 |
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| 245 | 1 | 0 | |a Defects of properties in mathematics : |b quantitative characterizations / |c Adrian I. Ban & Sorin G. Gal. |
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems. | |
| 650 | 0 | |a Mathematics. |0 http://id.loc.gov/authorities/subjects/sh85082139 | |
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| contents | Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems. |
| ctrlnum | (OCoLC)614463596 |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
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It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--Page 2 of cover.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. 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| id | ZDB-4-EBA-ocn614463596 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:36:43Z |
| institution | BVB |
| isbn | 9789812777645 9812777644 9789810249243 9810249241 |
| language | English |
| oclc_num | 614463596 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 352 pages) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific, |
| record_format | marc |
| series | Series on concrete and applicable mathematics ; |
| series2 | Series on concrete and applicable mathematics ; |
| spelling | Ban, Adrian I. https://id.oclc.org/worldcat/entity/E39PCjCDd7F7btF9rpRKVtb3HC http://id.loc.gov/authorities/names/no2002053919 Defects of properties in mathematics : quantitative characterizations / Adrian I. Ban & Sorin G. Gal. Singapore ; River Edge, NJ : World Scientific, ©2002. 1 online resource (xi, 352 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Series on concrete and applicable mathematics ; v. 5 Includes bibliographical references (pages 337-348) and index. "This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the "deviation from a (given) property", called the "defect of a property", in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics"--Page 2 of cover. Print version record. Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems. Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Fuzzy mathematics. http://id.loc.gov/authorities/subjects/sh98004034 Deviation (Mathematics) http://id.loc.gov/authorities/subjects/sh2002001969 Mathématiques. Mathématiques floues. Déviation (Mathématiques) applied mathematics. aat mathematics. aat MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Deviation (Mathematics) fast Fuzzy mathematics fast Mathematics fast Gal, Sorin G., 1953- https://id.oclc.org/worldcat/entity/E39PCjxmpxDQH799yTC9rc6R8C http://id.loc.gov/authorities/names/n99256513 has work: Defects of properties in mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCGkB8CqK33xwF7r8Bfb7h3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Ban, Adrian I. Defects of properties in mathematics. Singapore ; River Edge, NJ : World Scientific, ©2002 9810249241 9789810249243 (DLC) 2002514305 (OCoLC)50033967 Series on concrete and applicable mathematics ; v. 5. http://id.loc.gov/authorities/names/no2001065027 |
| spellingShingle | Ban, Adrian I. Defects of properties in mathematics : quantitative characterizations / Series on concrete and applicable mathematics ; Ch. 1. Introduction. 1.1. General description of the topic -- 1.2. On chapter 2: defect of property in set theory -- 1.3. On chapter 3: defect of property in topology -- 1.4. On chapter 4: defect of property in measure theory -- 1.5. On chapter 5: defect of property in real function theory -- 1.6. On chapter 6: defect of property in functional analysis -- 1.7. On chapter 7: defect of property in algebra -- 1.8. On chapter 8: miscellaneous -- ch. 2. Defect of property in set theory. 2.1. Measures of fuzziness -- 2.2. Intuitionistic entropies -- 2.3. Applications -- 2.4. Bibliographical remarks -- ch. 3. Defect of property in topology -- 3.1. Measures of noncompactness for classical sets -- 3.2. Random measures of noncompactness -- 3.3. Measures of noncompactness for fuzzy subsets in metric space -- 3.4. Measures of noncompactness for fuzzy subsets in topological space -- 3.5. Defects of opening and of closure for subsets in metric space -- 3.6. Bibliographical remarks and open problems -- ch. 4. Defect of property in measure theory -- 4.1. Defect of additivity: basic definitions and properties -- 4.2. Defect of complementarity -- 4.3. Defect of monotonicity -- 4.4. Defect of subadditivity and of superadditivity -- 4.5. Defect of measurability -- 4.6. Bibliographical remarks -- ch. 5. Defect of property in real function theory -- 5.1. Defect of continuity, of differentiability and of integrability -- 5.2. Defect of monotonicity, of convexity and of linearity -- 5.3. Defect of equality for inequalities -- 5.4. Bibliographical remarks and open problems -- ch. 6. Defect of property in functional analysis. 6.1. Defect of orthogonality in real normed spaces -- 6.2. Defect of property for sets in normed spaces -- 6.3. Defect of property for functional -- 6.4. Defect of property for linear operators on normed spaces -- 6.5. Defect of fixed point -- 6.6. Bibliographical remarks and open problems -- ch. 7. Defect of property in algebra -- 7.1. Defects of property for binary operations -- 7.2. Calculations of the defect of property -- 7.3. Defect of idempotency and distributivity of triangular norms -- 7.4. Applications -- 7.5. Bibliographical remarks -- ch. 8. Miscellaneous. 8.1. Defect of property in complex analysis -- 8.2. Defect of property in geometry -- 8.3. Defect of property in number theory -- 8.4. Defect of property in fuzzy logic -- 8.5. Bibliographical remarks and open problems. Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Fuzzy mathematics. http://id.loc.gov/authorities/subjects/sh98004034 Deviation (Mathematics) http://id.loc.gov/authorities/subjects/sh2002001969 Mathématiques. Mathématiques floues. Déviation (Mathématiques) applied mathematics. aat mathematics. aat MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Deviation (Mathematics) fast Fuzzy mathematics fast Mathematics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082139 http://id.loc.gov/authorities/subjects/sh98004034 http://id.loc.gov/authorities/subjects/sh2002001969 |
| title | Defects of properties in mathematics : quantitative characterizations / |
| title_auth | Defects of properties in mathematics : quantitative characterizations / |
| title_exact_search | Defects of properties in mathematics : quantitative characterizations / |
| title_full | Defects of properties in mathematics : quantitative characterizations / Adrian I. Ban & Sorin G. Gal. |
| title_fullStr | Defects of properties in mathematics : quantitative characterizations / Adrian I. Ban & Sorin G. Gal. |
| title_full_unstemmed | Defects of properties in mathematics : quantitative characterizations / Adrian I. Ban & Sorin G. Gal. |
| title_short | Defects of properties in mathematics : |
| title_sort | defects of properties in mathematics quantitative characterizations |
| title_sub | quantitative characterizations / |
| topic | Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Fuzzy mathematics. http://id.loc.gov/authorities/subjects/sh98004034 Deviation (Mathematics) http://id.loc.gov/authorities/subjects/sh2002001969 Mathématiques. Mathématiques floues. Déviation (Mathématiques) applied mathematics. aat mathematics. aat MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Deviation (Mathematics) fast Fuzzy mathematics fast Mathematics fast |
| topic_facet | Mathematics. Fuzzy mathematics. Deviation (Mathematics) Mathématiques. Mathématiques floues. Déviation (Mathématiques) applied mathematics. mathematics. MATHEMATICS Essays. MATHEMATICS Pre-Calculus. MATHEMATICS Reference. Fuzzy mathematics Mathematics |
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