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Some Structural Properties of the Set of Remote Points of a Metric Space

Published online by Cambridge University Press:  20 November 2018

Catherine L. Gates
Catherine L. Gates*
Affiliation:
Franklin and Marshall College, Lancaster, Pennsylvania
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A remote point of a metric space X is a point in βX |Xnot in the βX-closure of any discrete subset of X. Remote points have been studied by Fine and Gillman [2], Plank [4], Robinson [6], Woods [9, 10], Van Douwen [7] and others. The main results concerning the existence of remote points are listed in Section 1. In this paper we determine some structural properties of the set of remote points of a metric space which has no isolated points. The notation of Gillman and Jerison [3] and Walker [8] will be used. All spaces are assumed to be Tychonoff.

Let X be a space. The general remote points of X, denoted TX, are those points in βX |X which are not in the βX-closure of any nowhere dense sets of X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 195 - 209
Copyright
Copyright © Canadian Mathematical Society 1980

References

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