Relatively realcompact sets and nearly pseudocompact spaces
Schommer, John J.
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 375-382 / Harvested from Czech Digital Mathematics Library
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A space is said to be nearly pseudocompact iff $vX-X$ is dense in $\beta X-X$. In this paper relatively realcompact sets are defined, and it is shown that a space is nearly pseudocompact iff every relatively realcompact open set is relatively compact. Other equivalences of nearly pseudocompactness are obtained and compared to some results of Blair and van Douwen.

Publié le : 1993-01-01
Classification:  54C45,  54D30,  54D35,  54D45,  54D60,  54D99 
@article{118591,
     author = {John J. Schommer},
     title = {Relatively realcompact sets and nearly pseudocompact spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {375-382},
     zbl = {0781.54019},
     mrnumber = {1241747},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118591}
}

Schommer, John J. Relatively realcompact sets and nearly pseudocompact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 375-382. http://gdmltest.u-ga.fr/item/118591/

Blair R. On $v$-embedded sets in topological spaces, in ``TOPO 72 - General Topology and its Applications'', Second Pittsburg International Conference, December 18-22, 1972, Lecture Notes in Math., Springer-Verlag, Berlin-Heidelberg-New York, 1974, pp. 46-79. | MR 0358677

Blair R. Spaces in which special sets are $z$-embedded, Canadian Journal of Math. 28 (1976), 673-690. (1976) | MR 0420542 | Zbl 0359.54009

Blair R.; Van Douwen E. Nearly realcompact spaces, Topology Appl. 47, (1992), 209-221. (1992) | MR 1192310 | Zbl 0772.54021

Blair R.; Swardson M.A. Spaces with an Oz Stone-Čech compactification, Topology Appl. 36 (1990), 73-92. (1990) | MR 1062186 | Zbl 0721.54018

Engelking R. General Topology, Heldermann Verlag, Berlin, 1989. | MR 1039321 | Zbl 0684.54001

Gillman L.; Jerison M. Rings of Continuous Functions, University Series in Higher Math., Van Nostrand, Princeton, 1960. | MR 0116199 | Zbl 0327.46040

Henriksen M.; Rayburn M. On nearly pseudocompact spaces, Topology Appl. 11 (1980), 161-172. (1980) | MR 0572371 | Zbl 0419.54009

Mrówka S. Functionals on uniformly closed rings of continuous functions, Fund. Math. 46 (1958), 81-87. (1958) | MR 0100217

Negrepontis S. Baire sets in topological spaces, Arch. Math. 18 (1967), 603-608. (1967) | MR 0220248 | Zbl 0152.39703

Rayburn M. On hard sets, Topology Appl. 6 (1976), 21-26. (1976) | MR 0394577 | Zbl 0323.54022

Weir M. Hewitt-Nachbin Spaces, North-Holland Math. Studies 17, North-Holland and American Elsevier, Amsterdam and New York, 1975. | MR 0514909 | Zbl 0314.54002