Holdings: Geometric aspects of general topology

Geometric aspects of general topology:

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Bibliographic Details
Main Author:	Sakai, Katsuro (Author)
Format:	Electronic eBook
Language:	English
Published:	Tokyo [u.a.] Springer 2013
Series:	Springer monographs in mathematics
Subjects:	Geometrische Topologie
Online Access:	BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Abstract
Physical Description:	1 Online-Ressource
ISBN:	9784431543961 9784431543978
DOI:	10.1007/978-4-431-54397-8

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MARC


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adam_text	GEOMETRIC ASPECTS OF GENERAL TOPOLOGY / SAKAI, KATSURO : 2013 ABSTRACT / INHALTSTEXT THIS BOOK IS DESIGNED FOR GRADUATE STUDENTS TO ACQUIRE KNOWLEDGE OF DIMENSION THEORY, ANR THEORY (THEORY OF RETRACTS), AND RELATED TOPICS. THESE TWO THEORIES ARE CONNECTED WITH VARIOUS FIELDS IN GEOMETRIC TOPOLOGY AND IN GENERAL TOPOLOGY AS WELL. HENCE, FOR STUDENTS WHO WISH TO RESEARCH SUBJECTS IN GENERAL AND GEOMETRIC TOPOLOGY, UNDERSTANDING THESE THEORIES WILL BE VALUABLE. MANY PROOFS ARE ILLUSTRATED BY FIGURES OR DIAGRAMS, MAKING IT EASIER TO UNDERSTAND THE IDEAS OF THOSE PROOFS. ALTHOUGH EXERCISES AS SUCH ARE NOT INCLUDED, SOME RESULTS ARE GIVEN WITH ONLY A SKETCH OF THEIR PROOFS. COMPLETING THE PROOFS IN DETAIL PROVIDES GOOD EXERCISE AND TRAINING FOR GRADUATE STUDENTS AND WILL BE USEFUL IN GRADUATE CLASSES OR SEMINARS. RESEARCHERS SHOULD ALSO FIND THIS BOOK VERY HELPFUL, BECAUSE IT CONTAINS MANY SUBJECTS THAT ARE NOT PRESENTED IN USUAL TEXTBOOKS, E.G., DIM X × I = DIM X + 1 FOR A METRIZABLE SPACE X; THE DIFFERENCE BETWEEN THE SMALL AND LARGE INDUCTIVE DIMENSIONS; A HEREDITARILY INFINITE-DIMENSIONAL SPACE; THE ANR-NESS OF LOCALLY CONTRACTIBLE COUNTABLE-DIMENSIONAL METRIZABLE SPACES; AN INFINITE-DIMENSIONAL SPACE WITH FINITE COHOMOLOGICAL DIMENSION; A DIMENSION RAISING CELL-LIKE MAP; AND A NON-AR METRIC LINEAR SPACE. THE FINAL CHAPTER ENABLES STUDENTS TO UNDERSTAND HOW DEEPLY RELATED THE TWO THEORIES ARE. SIMPLICIAL COMPLEXES ARE VERY USEFUL IN TOPOLOGY AND ARE INDISPENSABLE FOR STUDYING THE THEORIES OF BOTH DIMENSION AND ANRS. THERE ARE MANY TEXTBOOKS FROM WHICH SOME KNOWLEDGE OF THESE SUBJECTS CAN BE OBTAINED, BUT NO TEXTBOOK DISCUSSES NON-LOCALLY FINITE SIMPLICIAL COMPLEXES IN DETAIL. SO, WHEN WE ENCOUNTER THEM, WE HAVE TO REFER TO THE ORIGINAL PAPERS. FOR INSTANCE, J.H.C. WHITEHEAD S THEOREM ON SMALL SUBDIVISIONS IS VERY IMPORTANT, BUT ITS PROOF CANNOT BE FOUND IN ANY TEXTBOOK. THE HOMOTOPY TYPE OF SIMPLICIAL COMPLEXES IS DISCUSSED IN TEXTBOOKS ON ALGEBRAIC TOPOLOGY USING CW COMPLEXES, BUT GEOMETRICAL ARGUMENTS USING SIMPLICIAL COMPLEXES ARE RATHER EASY DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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author	Sakai, Katsuro
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dewey-ones	514 - Topology
dewey-raw	514
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discipline	Informatik Mathematik
doi_str_mv	10.1007/978-4-431-54397-8
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indexdate	2024-07-10T00:43:52Z
institution	BVB
isbn	9784431543961 9784431543978
language	English
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spelling	Sakai, Katsuro Verfasser aut Geometric aspects of general topology Katsuro Sakai Tokyo [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Springer monographs in mathematics Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 s 1\p DE-604 https://doi.org/10.1007/978-4-431-54397-8 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026252908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Sakai, Katsuro Geometric aspects of general topology Geometrische Topologie (DE-588)4156724-9 gnd
subject_GND	(DE-588)4156724-9
title	Geometric aspects of general topology
title_auth	Geometric aspects of general topology
title_exact_search	Geometric aspects of general topology
title_full	Geometric aspects of general topology Katsuro Sakai
title_fullStr	Geometric aspects of general topology Katsuro Sakai
title_full_unstemmed	Geometric aspects of general topology Katsuro Sakai
title_short	Geometric aspects of general topology
title_sort	geometric aspects of general topology
topic	Geometrische Topologie (DE-588)4156724-9 gnd
topic_facet	Geometrische Topologie
url	https://doi.org/10.1007/978-4-431-54397-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026252908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT sakaikatsuro geometricaspectsofgeneraltopology

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