A Royal Road to Topology: Convergence of Filters
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Book Overview Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence th...
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.
The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.
Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book - from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.
The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.
Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Book Details Format: Hardcover | Pages: 732 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9811232105
FormatHardcover
Pages732
LanguageEnglish
ISBN9811232105
EAN9789811232107
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date1970-01-01
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight2.52 Pounds
Length9.0 Inches
Width6.0 Inches
Height1.56 Inches
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