Geometric aspects of general topology Katsuro Sakai

Format:

Book

Author/Creator:

Sakai, Katsuro

Series:

Springer monographs in mathematics

Language:

English

Subjects (All):

Topology.

Dimension theory (Topology).

Physical Description:

1 online resource

Place of Publication:

Tokyo New York Springer ©2013

System Details:

text file

PDF

Summary:

This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be useful in graduate classes or seminars. Researchers should also find this book very helpful, because it contains many subjects that are not presented in usual textbooks, e.g., dim X × I = dim X + 1 for a metrizable space X; the difference between the small and large inductive dimensions; a hereditarily infinite-dimensional space; the ANR-ness of locally contractible countable-dimensional metrizable spaces; an infinite-dimensional space with finite cohomological dimension; a dimension raising cell-like map; and a non-AR metric linear space. The final chapter enables students to understand how deeply related the two theories are. Simplicial complexes are very useful in topology and are indispensable for studying the theories of both dimension and ANRs. There are many textbooks from which some knowledge of these subjects can be obtained, but no textbook discusses non-locally finite simplicial complexes in detail. So, when we encounter them, we have to refer to the original papers. For instance, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any textbook. The homotopy type of simplicial complexes is discussed in textbooks on algebraic topology using CW complexes, but geometrical arguments using simplicial complexes are rather easy

Contents:

Preliminaries Metrization and Paracompact Spaces Topology of Linear Spaces and Convex Sets Simplicial Complexes and Polyhedra Dimensions of Spaces Retracts and Extensors Cell-Like Maps and Related Topics

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Geometric Aspects of General Topology

ISBN:

9784431543978

443154397X

OCLC:

856529443

Access Restriction:

Restricted for use by site license