## An embedding characterization of almost compact spaces

HTML articles powered by AMS MathViewer

- by Sergio Salbany PDF
- Trans. Amer. Math. Soc.
**275**(1983), 611-621 Request permission

## Abstract:

We characterize almost compact and almost realcompact spaces in terms of their situation in the product ${(J,u)^C}$. In the characterization of almost compactness $J$ is the two point set or the unit interval; in the characterization of almost realcompactness $J$ is the set of nonnegative integers or the nonnegative reals. $u$ is the upper topology on the real line restricted to $J$.## References

- Zdeněk Frolík,
*A generalization of realcompact spaces*, Czechoslovak Math. J.**13(88)**(1963), 127–138 (English, with Russian summary). MR**155289** - Z. Frolík and Chen-tung Liu,
*An embedding characterization of almost realcompact spaces*, Proc. Amer. Math. Soc.**32**(1972), 294–298. MR**290334**, DOI 10.1090/S0002-9939-1972-0290334-9 - Leonard Gillman and Meyer Jerison,
*Rings of continuous functions*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0116199**
K. Halpin, $H$- - S. Iliadis and S. Fomin,
*The method of concentric systems in the theory of topological spaces*, Uspehi Mat. Nauk**21**(1966), no. 4 (130), 47–76 (Russian). MR**0203677** - J. C. Kelly,
*Bitopological spaces*, Proc. London Math. Soc. (3)**13**(1963), 71–89. MR**143169**, DOI 10.1112/plms/s3-13.1.71 - Chen-tung Liu,
*Absolutely closed spaces*, Trans. Amer. Math. Soc.**130**(1968), 86–104. MR**219024**, DOI 10.1090/S0002-9947-1968-0219024-9 - C. T. Liu and G. E. Strecker,
*Concerning almost realcompactifications*, Czechoslovak Math. J.**22(97)**(1972), 181–190. MR**303507** - M. G. Murdeshwar and S. A. Naimpally,
*Quasi-uniform topological spaces*, P. Noordhoff Ltd., Groningen, 1966. MR**0211386** - Jack R. Porter,
*Categorical problems in minimal spaces*, Categorical topology (Proc. Conf., Mannheim, 1975) Lecture Notes in Math., Vol. 540, Springer, Berlin, 1976, pp. 482–500. MR**0438289** - Sergio Salbany,
*Bitopological spaces, compactifications and completions*, Mathematical Monographs of the University of Cape Town, No. 1, University of Cape Town, Department of Mathematics, Cape Town, 1974. MR**0425919** - Sergio Salbany,
*Reflective subcategories and closure operators*, Categorical topology (Proc. Conf., Mannheim, 1975) Lecture Notes in Math., Vol. 540, Springer, Berlin, 1976, pp. 548–565. MR**0451186** - S. Salbany,
*An embedding characterization of compact spaces*, Categorical topology (Proc. Internat. Conf., Free Univ. Berlin, Berlin, 1978) Lecture Notes in Math., vol. 719, Springer, Berlin, 1979, pp. 316–325. MR**544656**

*closed spaces and almost compact spaces*, M. Sc. thesis. University of Cape Town, 1974.

## Additional Information

- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**275**(1983), 611-621 - MSC: Primary 54D30; Secondary 54D60
- DOI: https://doi.org/10.1090/S0002-9947-1983-0682721-3
- MathSciNet review: 682721