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Discrete Sets and Discrete Maps

Published online by Cambridge University Press:  20 November 2018

Richard H. Warren
Richard H. Warren*
Affiliation:
Department of Mathematics and Computer Science, University of Nebraska at Omaha, Omaha, Ne 68182
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Abstract

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A subset of a topological space is called discrete iff every point in the space has a neighborhood which meets the set in at most one point. Discrete sets are useful for decomposing the images of certain maps and for generalizing closed maps. All discrete sets are closed iff the space is T1. As a result of characterizing discrete and countably discrete maps, theorems due to Vaĭnšteĭn and Engelking are extended to these maps.

Keywords

54C1054A25discrete setcountably discrete setgeneralizations of closed map
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 242 - 244
Copyright
Copyright © Canadian Mathematical Society 1982

References

[A] Arhangel'skiĭ, A.. On closed mappings, bicompact spaces, and a problem of P. Aleksandrov, Pacific J. Math. 18 (1966), 201-208.Google Scholar
[E] R., Engelking, Closed mappings on complete metric spaces, Fund. Math. 70 (1971), 103-107.Google Scholar
[T] T., Tani, Some generalizations of closed maps, their properties and M-spaces, Math. Japon. 20 (1975), 237-252.Google Scholar