A Royal Road to Topology: Convergence of Filters - Hardcover

Dolecki Szymon

Hardcover

ISBN 10: 9811232105 ISBN 13: 9789811232107

Publisher: World Scientific Pub Co Inc, 2024

Synopsis

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.

Edition details

• Publisher: World Scientific Pub Co Inc
• Publication date: 2024
• Language: English
• ISBN 10: 9811232105
• ISBN 13: 9789811232107
• Binding: Hardcover
• Number of pages: 710