Non-Tychonoff 
-compactifiable spaces
Authors:
K. P. Hart and J. Vermeer
Journal:
Proc. Amer. Math. Soc. 89 (1983), 725-729
MSC:
Primary 54D30; Secondary 54C10, 54D25, 54G20
DOI:
https://doi.org/10.1090/S0002-9939-1983-0719005-6
MathSciNet review:
719005
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Abstract | References | Similar Articles | Additional Information
Abstract: We construct a non-Tychonoff space 
which is 
-compactifiable, thus answering a question of S. Hechler. We also answer a question of R. M. Stephenson: whether there exists a Tychonoff space, the largest 
-compactification of which has a noncompact semiregularization.
- [BS] M. P. Berri and R. H. Sorgenfrey, Minimal regular spaces, Proc. Amer. Math. Soc. 14 (1963), 454-458. MR 0152978 (27:2949)
- [Ch] J. Chaber, Remarks on open-closed mappings, Fund. Math. 73 (1971), 197-208. MR 0303487 (46:2624)
- [He] S. H. Hechler, On a notion of weak compactness in non-regular spaces, Studies in Topology (N. M. Stavrakas and K. R. Allen, eds.), Academic Press, New York, 1975, pp. 215-237. MR 0358692 (50:11151)
- [St]
R. M. Stephenson, Not every minimal Hausdorff space is
-compact, Proc. Amer. Math. Soc. 52 (1975), 381-388. MR 0423296 (54:11276)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0719005-6
Keywords:
-compactifiable spaces,
perfect maps
Article copyright:
© Copyright 1983
American Mathematical Society
