Regular-closed, Urysohn-closed and completely Hausdorff-closed spaces.
Author:
H. Herrlich
Journal:
Proc. Amer. Math. Soc. 26 (1970), 695-698
MSC:
Primary 54.22
DOI:
https://doi.org/10.1090/S0002-9939-1970-0268838-2
MathSciNet review:
0268838
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Abstract | References | Similar Articles | Additional Information
Abstract: Recently M. P. Berri, J. R. Porter, and R. M. Stephenson, Jr. have given a survey on $P$-closed and $P$-minimal spaces. In the present paper the first two problems of this survey will be solved: (1) The product of two Urysohn-closed spaces need not be Urysohn-closed. (2) A completely Hausdorff-closed regular space need not be regular-closed.
- Manuel P. Berri, Minimal topological spaces, Trans. Amer. Math. Soc. 108 (1963), 97–105. MR 150724, DOI https://doi.org/10.1090/S0002-9947-1963-0150724-0 M. P. Berri, J. R. Porter and R. M. Stephenson, Jr., A survey of minimal topological spaces, Proc. India Topology Conference, Kanpur, 1968 (to appear).
- Horst Herrlich, $T_{v}$-Abgeschlossenheit und $T_{v}$-Minimalität, Math. Z. 88 (1965), 285–294 (German). MR 184191, DOI https://doi.org/10.1007/BF01111687
- Jack Porter and John Thomas, On $H$-closed and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 138 (1969), 159–170. MR 238268, DOI https://doi.org/10.1090/S0002-9947-1969-0238268-4
- C. T. Scarborough and A. H. Stone, Products of nearly compact spaces, Trans. Amer. Math. Soc. 124 (1966), 131–147. MR 203679, DOI https://doi.org/10.1090/S0002-9947-1966-0203679-7
- C. T. Scarborough and R. M. Stephenson, Minimal topologies, Colloq. Math. 19 (1968), 215–219. MR 227938, DOI https://doi.org/10.4064/cm-19-2-215-219 R. M. Stephenson, Jr., $P$-minimal and $P$-closed spaces, Thesis, Tulane University, New Orleans, La., 1967. ---, Remarks on minimal topological spaces, Notices Amer. Math. Soc. 13 (1966), 256. Abstract #66T-163.
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Keywords:
Urysohn-closed spaces,
regular-closed spaces,
completely Hausdorff-closed spaces,
minimal topological spaces,
products
Article copyright:
© Copyright 1970
American Mathematical Society