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Accumulation Points of Continuous Realvalued Functions and Compactifications

Published online by Cambridge University Press:  20 November 2018

Eng Ung Choo
Eng Ung Choo*
Affiliation:
Department of Mathematics, University of British Columbia, VancouverB.C.
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All topological spaces are assumed to be completely regular. C(X) (resp. C*(X)) will denote the ring of all (resp. all bounded) continuous real-valued functions on X. βX is the Stone-Cech compactification of X. A real number t is said to be an accumulation point of a function f ∊ C(X) if and only if f-1[[t-ε, t + ε]] is not compact for every ε > 0.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 47 - 52
Copyright
Copyright © Canadian Mathematical Society 1977

References

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