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Hyperspaces of H-Closed Spaces

Published online by Cambridge University Press:  20 November 2018

L. M. Friedler ,
R. F. Dickman Jr.  and
R. L. Krystock
L. M. Friedler
Affiliation:
College of St. Scholastica, Duluth, Minnesota
R. F. Dickman Jr.
Affiliation:
Virginia Polytechnic Institute, Blacksburg, Virginia
R. L. Krystock
Affiliation:
Virginia Polytechnic Institute, Blacksburg, Virginia
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A space is H(i) [R(i)] if every open [regular] filter base has a cluster point and H(ii) [R(ii)] if every open [regular] filter base with a unique cluster point converges. This terminology is due to C. T. Scarborough and A. H. Stone [11]; H(i) spaces have been studied as quasi-H-closed spaces in [10] and as generalized absolutely closed spaces in [6]. Hausdorff H(i) [H(ii)] spaces are called H-closed [minimal Hausdorff] and regular T1 R(i) [R(ii)] spaces are called R-closed [minimal regular]. For a space X, 2X is the set of all non-empty closed subsets of X with the finite topology [8]. The present study was motivated by the longstanding problem of whether or not a T3 space with every closed subset R-closed is compact, and also by the well-known result ([8] and [14]) that X is compact if and only if 2X is compact.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 5 , 01 October 1980 , pp. 1072 - 1079
Copyright
Copyright © Canadian Mathematical Society 1980

References

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