Royal Road To Topology: Convergence Of Filters
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A01=Szymon Dolecki
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Author_Szymon Dolecki
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Category1=Non-Fiction
Category=PBP
Compactness
Completeness
Continuity
Convergence
COP=Singapore
Delivery_Delivery within 10-20 working days
eq_isMigrated=0
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Filter
Functional Convergence
Hyperspace
Language_English
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Pretopology
Price_€100 and above
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Pseudotopology
softlaunch
Topology
Product details
- ISBN 9789811232107
- Publication Date: 31 Jan 2024
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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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.
