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Keywords:
maximal pseudocompact; maximal feebly compact; submaximal topology
maximal pseudocompact; maximal feebly compact; submaximal topology
Summary:
Maximal pseudocompact spaces (i.e. pseudocompact spaces possessing no strictly stronger pseudocompact topology) are characterized. It is shown that submaximal pseudocompact spaces whose pseudocompact subspaces are closed need not be maximal pseudocompact. Various techniques for constructing maximal pseudocompact spaces are described. Maximal pseudocompactness is compared to maximal feeble compactness.
References:
[Bi] Bing R.H.: A connected countable Hausdorff space. Proc. Amer. Math. Soc. 4 (1953), 474. MR 0060806 | Zbl 0051.13902
[Bo] Bourbaki N.: Elements of Mathematics, General Topology, Part I. Addison-Wesley Reading (1966).
[Ca$_1$] Douglas Cameron: Maximal and minimal topologies. Trans. Amer. Math. Soc. 160 (1971), 229-248. MR 0281142
[Ca$_2$] Douglas Cameron: A class of maximal topologies. Pacific J. Math 70 (1977), 101-104. MR 0464157
[Ca$_3$] Douglas Cameron: A note on maximal pseudocompactness. Bull. Malaysian Math. Soc. (2) 2 (1979), No. 1, 45-46. MR 0545803
[Ca$_4$] Douglas Cameron: A survey of maximal topological spaces. Topology Proceedings 2 (1977), 11-60. MR 0540596
[Ca$_5$] Douglas Cameron: $\Delta$-maximal topologies for some cardinal functions. Gen. Top. Applic. 9 (1978), 59-70. MR 0500832
[E] Engelking R.: General Topology. Polish Scientific Publishers Warsaw (1977). MR 0500780 | Zbl 0373.54002
[GJ] Gillman L., Jerison M.: Rings of continuous functions. Van Nostrand Princeton (1960). MR 0116199 | Zbl 0093.30001
[GS] Guthrie J.A., Stone H.E.: Pseudocompactness and invariance of continuity. Gen. Top. Applic. 7 (1977), 1-13. MR 0442872 | Zbl 0345.54017
[Hec] Hechler S.H.: Two ${\bold R}$-closed spaces revisited. Proc. Amer. Math. Soc. 56 (1976), 303-309. MR 0405354
[Her] Herrlich H.: $T_\upsilon$-Abgeschlossenheit and $T_\upsilon$-Minimalität. Math. Zeit. 88 (1965), 285-294. MR 0184191
[Ho] Hodel R.: Cardinal functions I, Handbook of Set-theoretic Topology. Kunen, Vaughan North-Holland, Amsterdam (1984), 1-61. MR 0776620
[M] Mandelker M.: Supports of continuous functions. Trans. Amer. Math. Soc. 156 (1971), 73-83. MR 0275367 | Zbl 0197.48703
[PSW$_1$] Porter J.R., Stephenson R.M., Jr., and Woods R.G.: Maximal feebly compact spaces. Topology Applic. \toappear.
[PSW$_2$] Porter J.R., Stephenson R.M., Jr., and Woods R.G.: Spaces with maximal feebly compact expansions. preprint.
[PV] Porter J.R., Vermeer J.: Spaces with coarser minimal Hausdorff topologies. Trans. Amer. Math. Soc. 289 (1985), 59-71. MR 0779052 | Zbl 0577.54019
[PW] Porter J.R., Woods R.G.: Extensions and Absolutes of Hausdorff spaces. Springer-Verlag New York (1988). MR 0918341 | Zbl 0652.54016
[R] Raha A.B.: Maximal topologies. J. Austral. Math. Soc. 15 (1973), 279-290. MR 0324646 | Zbl 0267.54018
[St$_1$] Stephenson R.M., Jr.: Pseudocompact spaces. Trans. Amer. Math. Soc. 134 (1968), 437-448. MR 0232349 | Zbl 0169.53903
[St$_2$] Stephenson R.M., Jr.: Minimal first countable topologies. Trans. Amer. Math. Soc. 138 (1969), 115-127. MR 0238261 | Zbl 0175.19702
[St$_4$] Stephenson R.M., Jr.: Two ${\bold R}$-closed spaces. Canad. J. Math. 24 (1972), 286-292. MR 0298613
[W] Weston J.D.: On the comparison of topologies. J. Lond. Math. Soc. 37 (1957), 342-354. MR 0094776 | Zbl 0078.36002
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