Bell, Murray G. First countable pseudocompactifications. (English) Zbl 0568.54019 Topology Appl. 21, 159-166 (1985). A general construction for creating first countable pseudo-compact extensions of certain spaces is given. We show that there exists a first countable \(\sigma\)-compact space with no first countable pseudocompactification. We construct a new Suslinean example, namely, a first countable, pseudocompact, ccc, non-separable space. Assuming Martin’s axiom, we can further achieve a point-countable base. A second application is to unify and clarify examples of B. Scott [Topology Proc. 4, No.2, 577-587 (1979; Zbl 0449.54020)] and W. S. Watson [A pseudocompact meta-Lindelöf space which is not compact (to appear)] of pseudocompact, meta-Lindelöf and point-countable base non-compact spaces. Cited in 1 ReviewCited in 7 Documents MSC: 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54G20 Counterexamples in general topology 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) Keywords:pseudocompact, meta-Lindelöf non-compact spaces; first countable pseudo-compact extensions; first countable \(\sigma \) -compact space; first countable pseudocompactification; first countable, pseudocompact, ccc, non-separable space; Martin’s axiom; point-countable base non- compact spaces Citations:Zbl 0449.54020 PDFBibTeX XMLCite \textit{M. G. Bell}, Topology Appl. 21, 159--166 (1985; Zbl 0568.54019) Full Text: DOI References: [1] Aquaro, G., Point-countable open coverings in countably compact spaces, General Topology and Its Relations to Modern Analysis and Algebra II, 39-41 (1966), Prague [2] Bell, M. G., A normal first countable ccc nonseparable space, Proc. Amer. Math. Soc., 74, 1, 151-155 (1979) · Zbl 0371.54041 [3] van Douwen, E., The Pixley-Roy topology on spaces of subsets, Set-Theoretic Topology, 111-134 (1977) · Zbl 0372.54006 [4] Jech, J., Nonprovability of Souslin’s hypothesis, Comment. Math. Univ. Carolinae, 8, 293-296 (1967) [5] Juhasz, I., Consistency results in topology, (Barwise, J., Handbook of Mathematical Logic (1977), North-Holland: North-Holland Amsterdam) · Zbl 0257.54003 [6] Kuratowski, K., Topology, Vol. 1 (1966), Academic Press: Academic Press New York [7] Miscenko, A. S., Spaces with a point-countable base, Soviet Math. Dokl., 3, 855-858 (1962) · Zbl 0122.17304 [8] Pixley, C.; Roy, P., Uncompletable Moore spaces, Proc. Auburn Univ. Conf. (1969), Auburn, AL · Zbl 0259.54022 [9] Rudin, M. E., Concerning abstract spaces, Duke Math. J., 17, 317-327 (1950) · Zbl 0039.39303 [10] Sapirovskii, B., On the tightness, π-weight and related notions…,, Uc. Zap. Latv. Univ., 247, 88-89 (1976), (in Russian) [11] Scott, B., Pseudocompact metacompact spaces are compact, Topology Proc., 4, 577-586 (1979) · Zbl 0449.54020 [14] Mrowka, S., On completely regular spaces, Fund. Math., 41, 105-106 (1954) · Zbl 0055.41304 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.