Compactifications with countable remainder
Author:
M. G. Charalambous
Journal:
Proc. Amer. Math. Soc. 78 (1980), 127-131
MSC:
Primary 54D40; Secondary 54D35
DOI:
https://doi.org/10.1090/S0002-9939-1980-0548099-3
MathSciNet review:
548099
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we deal with the problem of characterizing those spaces that have a compactification with countable remainder.
- [1] M. G. Charalambous, Spaces with increment of dimension n, Fund. Math. 93 (1976), 97-107. MR 0433411 (55:6387)
- [2] M. Henriksen, Tychonoff spaces that have a compactification with a countable remainder, General Topology and its Relations to Modern Analysis and Algebra, IV (Proc. Fourth Prague Topological Sympos., Prague, 1976), Part B, Soc. Czech. Mathematicians and Physicists, Prague, 1977, pp. 164-167. MR 0454922 (56:13165)
- [3] T. Hoshina, Compactifications by adding a countable number of points, General Topology and its Relations to Modern Analysis and Algebra, IV, Part B, Soc. Czech. Mathematicians and Physicists, Prague, 1977, pp. 168-169. MR 0461446 (57:1431)
- [4] -, Countable-points compactifications for metric spaces, preprint.
- [5] J. R. Isbell, Uniform spaces, Math. Surveys, no. 12, Amer. Math. Soc., Providence, R. I., 1964. MR 0170323 (30:561)
- [6] K. Morita, On bicompactifications of semibicompact spaces, Sci. Rep. Tokyo Bunrika Daigaku, Sect. A 4 (1952), 222-229. MR 0052089 (14:571d)
- [7] L. A. Steen and J. A. Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, New York, 1970. MR 0266131 (42:1040)
- [8] T. Terada, On countable discrete compactifications, General Topology and Appl. 7 (1977), 321-327. MR 0500840 (58:18354)
- [9] R. C. Walker, The Stone-Čech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York and Berlin, 1974. MR 0380698 (52:1595)
- [10] L. Zippin, On semicompact spaces, Amer. J. Math. 57 (1935), 327-341. MR 1507076
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D40, 54D35
Retrieve articles in all journals with MSC: 54D40, 54D35
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1980-0548099-3
Keywords:
Rim-compact,
Cech-complete,
network,
countable compactification,
small inductive dimension,
covering dimension
Article copyright:
© Copyright 1980
American Mathematical Society
