An embedding characterization of almost compact spaces

Salbany, Sergio

doi:10.1090/S0002-9947-1983-0682721-3

An embedding characterization of almost compact spaces
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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

closed spaces and almost compact spaces

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