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
Full-text PDF Free Access
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] Manuel P. Berri and R. H. Sorgenfrey, Minimal regular spaces, Proc. Amer. Math. Soc. 14 (1963), 454–458. MR 0152978, https://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
- [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
- [St] R. M. Stephenson Jr., Not every minimal Hausdorff space is 𝑒-compact, Proc. Amer. Math. Soc. 52 (1975), 381–389. MR 0423296, https://doi.org/10.1090/S0002-9939-1975-0423296-4
-compact, Proc. Amer. Math. Soc. 52 (1975), 381-388. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D30, 54C10, 54D25, 54G20
Retrieve articles in all journals with MSC: 54D30, 54C10, 54D25, 54G20
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