Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
346 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators |
| Beschreibung: | 1 Online-Ressource (XVIII, 358 p) |
| ISBN: | 9789401584005 9789048146314 |
| DOI: | 10.1007/978-94-015-8400-5 |
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| 500 | |a Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators | ||
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| isbn | 9789401584005 9789048146314 |
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| spelling | Dikranjan, D. Verfasser aut Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics by D. Dikranjan, W. Tholen Dordrecht Springer Netherlands 1995 1 Online-Ressource (XVIII, 358 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 346 Our motivation for gathering the material for this book over aperiod of seven years has been to unify and simplify ideas wh ich appeared in a sizable number of re search articles during the past two decades. More specifically, it has been our aim to provide the categorical foundations for extensive work that was published on the epimorphism- and cowellpoweredness problem, predominantly for categories of topological spaces. In doing so we found the categorical not ion of closure operators interesting enough to be studied for its own sake, as it unifies and describes other significant mathematical notions and since it leads to a never-ending stream of ex amples and applications in all areas of mathematics. These are somewhat arbitrarily restricted to topology, algebra and (a small part of) discrete mathematics in this book, although other areas, such as functional analysis, would provide an equally rich and interesting supply of examples. We also had to restrict the themes in our theoretical exposition. In spite of the fact that closure operators generalize the uni versal closure operations of abelian category theory and of topos- and sheaf theory, we chose to mention these aspects only en passant, in favour of the presentation of new results more closely related to our original intentions. We also needed to refrain from studying topological concepts, such as compactness, in the setting of an arbitrary closure-equipped category, although this topic appears prominently in the published literature involving closure operators Mathematics Algebra Group theory Topological Groups Topology Category Theory, Homological Algebra Group Theory and Generalizations Topological Groups, Lie Groups Order, Lattices, Ordered Algebraic Structures Mathematik Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Abgeschlossener linearer Operator (DE-588)4141055-5 gnd rswk-swf Abgeschlossener linearer Operator (DE-588)4141055-5 s Kategorientheorie (DE-588)4120552-2 s 1\p DE-604 Tholen, W. Sonstige oth https://doi.org/10.1007/978-94-015-8400-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dikranjan, D. Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics Mathematics Algebra Group theory Topological Groups Topology Category Theory, Homological Algebra Group Theory and Generalizations Topological Groups, Lie Groups Order, Lattices, Ordered Algebraic Structures Mathematik Kategorientheorie (DE-588)4120552-2 gnd Abgeschlossener linearer Operator (DE-588)4141055-5 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4141055-5 |
| title | Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics |
| title_auth | Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics |
| title_exact_search | Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics |
| title_full | Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics by D. Dikranjan, W. Tholen |
| title_fullStr | Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics by D. Dikranjan, W. Tholen |
| title_full_unstemmed | Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics by D. Dikranjan, W. Tholen |
| title_short | Categorical Structure of Closure Operators |
| title_sort | categorical structure of closure operators with applications to topology algebra and discrete mathematics |
| title_sub | With Applications to Topology, Algebra and Discrete Mathematics |
| topic | Mathematics Algebra Group theory Topological Groups Topology Category Theory, Homological Algebra Group Theory and Generalizations Topological Groups, Lie Groups Order, Lattices, Ordered Algebraic Structures Mathematik Kategorientheorie (DE-588)4120552-2 gnd Abgeschlossener linearer Operator (DE-588)4141055-5 gnd |
| topic_facet | Mathematics Algebra Group theory Topological Groups Topology Category Theory, Homological Algebra Group Theory and Generalizations Topological Groups, Lie Groups Order, Lattices, Ordered Algebraic Structures Mathematik Kategorientheorie Abgeschlossener linearer Operator |
| url | https://doi.org/10.1007/978-94-015-8400-5 |
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