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Title: Maximal pseudocompact spaces (English)
Author: Porter, Jack R.
Author: Stephenson, R. M., Jr.
Author: Woods, Grant R.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 35
Issue: 1
Year: 1994
Pages: 127-145
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Category: math
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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. (English)
Keyword: maximal pseudocompact
Keyword: maximal feebly compact
Keyword: submaximal topology
MSC: 54A10
MSC: 54C30
idZBL: Zbl 0804.54004
idMR: MR1292589
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Date available: 2009-01-08T18:09:24Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118647
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Reference: [Bi] Bing R.H.: A connected countable Hausdorff space.Proc. Amer. Math. Soc. 4 (1953), 474. Zbl 0051.13902, MR 0060806
Reference: [Bo] Bourbaki N.: Elements of Mathematics, General Topology, Part I.Addison-Wesley Reading (1966).
Reference: [Ca$_1$] Douglas Cameron: Maximal and minimal topologies.Trans. Amer. Math. Soc. 160 (1971), 229-248. MR 0281142
Reference: [Ca$_2$] Douglas Cameron: A class of maximal topologies.Pacific J. Math 70 (1977), 101-104. MR 0464157
Reference: [Ca$_3$] Douglas Cameron: A note on maximal pseudocompactness.Bull. Malaysian Math. Soc. (2) 2 (1979), No. 1, 45-46. MR 0545803
Reference: [Ca$_4$] Douglas Cameron: A survey of maximal topological spaces.Topology Proceedings 2 (1977), 11-60. MR 0540596
Reference: [Ca$_5$] Douglas Cameron: $\Delta$-maximal topologies for some cardinal functions.Gen. Top. Applic. 9 (1978), 59-70. MR 0500832
Reference: [E] Engelking R.: General Topology.Polish Scientific Publishers Warsaw (1977). Zbl 0373.54002, MR 0500780
Reference: [GJ] Gillman L., Jerison M.: Rings of continuous functions.Van Nostrand Princeton (1960). Zbl 0093.30001, MR 0116199
Reference: [GS] Guthrie J.A., Stone H.E.: Pseudocompactness and invariance of continuity.Gen. Top. Applic. 7 (1977), 1-13. Zbl 0345.54017, MR 0442872
Reference: [Hec] Hechler S.H.: Two ${\bold R}$-closed spaces revisited.Proc. Amer. Math. Soc. 56 (1976), 303-309. MR 0405354
Reference: [Her] Herrlich H.: $T_\upsilon$-Abgeschlossenheit and $T_\upsilon$-Minimalität.Math. Zeit. 88 (1965), 285-294. MR 0184191
Reference: [Ho] Hodel R.: Cardinal functions I, Handbook of Set-theoretic Topology.Kunen, Vaughan North-Holland, Amsterdam (1984), 1-61. MR 0776620
Reference: [M] Mandelker M.: Supports of continuous functions.Trans. Amer. Math. Soc. 156 (1971), 73-83. Zbl 0197.48703, MR 0275367
Reference: [PSW$_1$] Porter J.R., Stephenson R.M., Jr., and Woods R.G.: Maximal feebly compact spaces.Topology Applic. \toappear.
Reference: [PSW$_2$] Porter J.R., Stephenson R.M., Jr., and Woods R.G.: Spaces with maximal feebly compact expansions.preprint.
Reference: [PV] Porter J.R., Vermeer J.: Spaces with coarser minimal Hausdorff topologies.Trans. Amer. Math. Soc. 289 (1985), 59-71. Zbl 0577.54019, MR 0779052
Reference: [PW] Porter J.R., Woods R.G.: Extensions and Absolutes of Hausdorff spaces.Springer-Verlag New York (1988). Zbl 0652.54016, MR 0918341
Reference: [R] Raha A.B.: Maximal topologies.J. Austral. Math. Soc. 15 (1973), 279-290. Zbl 0267.54018, MR 0324646
Reference: [St$_1$] Stephenson R.M., Jr.: Pseudocompact spaces.Trans. Amer. Math. Soc. 134 (1968), 437-448. Zbl 0169.53903, MR 0232349
Reference: [St$_2$] Stephenson R.M., Jr.: Minimal first countable topologies.Trans. Amer. Math. Soc. 138 (1969), 115-127. Zbl 0175.19702, MR 0238261
Reference: [St$_4$] Stephenson R.M., Jr.: Two ${\bold R}$-closed spaces.Canad. J. Math. 24 (1972), 286-292. MR 0298613
Reference: [W] Weston J.D.: On the comparison of topologies.J. Lond. Math. Soc. 37 (1957), 342-354. Zbl 0078.36002, MR 0094776
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