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Mathematics and Its Applications

Categorical Structure of Closure Operators

With Applications to Topology, Algebra and Discrete Mathematics

Authors: Dikranjan, Dikran, Tholen, Walter

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eBook 101,14 €
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  • ISBN 978-94-015-8400-5
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Hardcover 124,79 €
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  • ISBN 978-0-7923-3772-0
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  • ISBN 978-90-481-4631-4
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About this book

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.

Reviews

` ... substantial enrichment of the literature on closure operators. Anybody working in this field should look into it; in the reviewer's opinion such a look will in most cases be rewarded. ... recommended to mathematicians ... best suited for graduate students and research mathematicians.'
Mathematical Reviews Clippings 97i

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-94-015-8400-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-0-7923-3772-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-90-481-4631-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Categorical Structure of Closure Operators
Book Subtitle
With Applications to Topology, Algebra and Discrete Mathematics
Authors
Series Title
Mathematics and Its Applications
Series Volume
346
Copyright
1995
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-8400-5
DOI
10.1007/978-94-015-8400-5
Hardcover ISBN
978-0-7923-3772-0
Softcover ISBN
978-90-481-4631-4
Edition Number
1
Number of Pages
XVIII, 358
Topics