Dimension Theory

Beschreibung

This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions.
Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions.

Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.

Presupposed topological definitions and facts are carefully recalled Includes numerous exercises proving presupposed facts Includes numerous exercises of further interest Helpful hints accompany exercises where necessary Includes plenty of material that cannot be found elsewhere

Autor*in

Michael G. Charalambous

Themen in »Dimension Theory«

covering dimension inductive dimension metric spaces normal spaces perfectly normal spaces Tychonoff spaces Lindelof spaces N-compact spaces dimension theory

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“The monograph contains a great deal of useful and up-to-date material on dimension theory; the exposition is transparent and well organized which makes it possible to use this work both as a textbook of dimension theory and a base of research projects in numerous areas.” (Vladimir Tkachuk, zbMATH 1471.54001, 2021)
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