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Local Topological Properties of Maps and Open Extensions of Maps

Published online by Cambridge University Press:  20 November 2018

J. K. Kohli
J. K. Kohli*
Affiliation:
Hindu College, University of Delhi, Delhi 110007, India
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A σ-discrete set in a topological space is a set which is a countable union of discrete closed subsets. A mapping ƒ : X ⟶ Y from a topological space X into a topological space Y is said to be σ-discrete (countable) if each fibre ƒ-1(y), y ϵ Y is σ-discrete (countable). In 1936, Alexandroff showed that every open map of a bounded multiplicity between Hausdorff spaces is a local homeomorphism on a dense open subset of the domain [2].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1121 - 1128
Copyright
Copyright © Canadian Mathematical Society 1977

References

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