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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
MathSciNet review:
719005
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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]
Manuel
P. Berri and R.
H. Sorgenfrey, Minimal regular spaces, Proc. Amer. Math. Soc. 14 (1963), 454–458. MR 0152978
(27 #2949), http://dx.doi.org/10.1090/S0002-9939-1963-0152978-9
- [Ch]
J.
Chaber, Remarks on open-closed mappings, Fund. Math.
74 (1972), no. 3, 197–208. MR 0303487
(46 #2624)
- [He]
Stephen
H. Hechler, On a notion of weak compactness in non-regular
spaces, Studies in topology (Proc. Conf., Univ. North Carolina,
Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.),
Academic Press, New York, 1975, pp. 215–237. MR 0358692
(50 #11151)
- [St]
R.
M. Stephenson Jr., Not every minimal Hausdorff space is
𝑒-compact, Proc. Amer. Math. Soc.
52 (1975),
381–389. MR 0423296
(54 #11276), http://dx.doi.org/10.1090/S0002-9939-1975-0423296-4
- [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:
http://dx.doi.org/10.1090/S0002-9939-1983-0719005-6
PII:
S 0002-9939(1983)0719005-6
Keywords:
 -compactifiable spaces,
perfect maps
Article copyright:
© Copyright 1983 American Mathematical Society
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