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Homotopy and Isotopy Properties of Topological Spaces

Published online by Cambridge University Press:  20 November 2018

Sze-Tsen Hu
Sze-Tsen Hu*
Affiliation:
University of California at Los Angeles
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The most important notion in topology is that of a homeomorphism f: X → Y from a topological space X onto a topological space Y. If a homeomorphism f: X → Y exists, then the topological spaces X and F are said to be homeomorphic (or topologically equivalent), in symbols,

X ≡ Y.

The relation ≡ among topological spaces is obviously reflexive, symmetric, and transitive; hence it is an equivalence relation. For an arbitrary family F of topological spaces, this equivalence relation ≡ divides /Mnto disjoint equivalence classes called the topology types of the family F. Then, the main problem in topology is the topological classification problem formulated as follows.

The topological classification problem: Given a family F of topological spaces, find an effective enumeration of the topology types of the family F and exhibit a representative space in each of these topology types.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 167 - 176
Copyright
Copyright © Canadian Mathematical Society 1961

References

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