Maximal pseudocompact spaces

Jack R. Porter; Robert M., Jr. Stephenson; Grant R. Woods

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 1, page 127-145
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Porter, Jack R., Stephenson, Robert M., Jr., and Woods, Grant R.. "Maximal pseudocompact spaces." Commentationes Mathematicae Universitatis Carolinae 35.1 (1994): 127-145. <http://eudml.org/doc/247607>.

@article{Porter1994,
abstract = {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.},
author = {Porter, Jack R., Stephenson, Robert M., Jr., Woods, Grant R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {maximal pseudocompact; maximal feebly compact; submaximal topology; submaximal topology; maximal pseudocompact spaces; maximal feebly compact spaces},
language = {eng},
number = {1},
pages = {127-145},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Maximal pseudocompact spaces},
url = {http://eudml.org/doc/247607},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Porter, Jack R.
AU - Stephenson, Robert M., Jr.
AU - Woods, Grant R.
TI - Maximal pseudocompact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 1
SP - 127
EP - 145
AB - 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.
LA - eng
KW - maximal pseudocompact; maximal feebly compact; submaximal topology; submaximal topology; maximal pseudocompact spaces; maximal feebly compact spaces
UR - http://eudml.org/doc/247607
ER -

References

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  1. Bing R.H., A connected countable Hausdorff space, Proc. Amer. Math. Soc. 4 (1953), 474. (1953) Zbl0051.13902MR0060806
  2. Bourbaki N., Elements of Mathematics, General Topology, Part I, Addison-Wesley Reading (1966). (1966) 
  3. Douglas Cameron, Maximal and minimal topologies, Trans. Amer. Math. Soc. 160 (1971), 229-248. (1971) MR0281142
  4. Douglas Cameron, A class of maximal topologies, Pacific J. Math 70 (1977), 101-104. (1977) MR0464157
  5. Douglas Cameron, A note on maximal pseudocompactness, Bull. Malaysian Math. Soc. (2) 2 (1979), No. 1, 45-46. (1979) MR0545803
  6. Douglas Cameron, A survey of maximal topological spaces, Topology Proceedings 2 (1977), 11-60. (1977) MR0540596
  7. Douglas Cameron, Δ -maximal topologies for some cardinal functions, Gen. Top. Applic. 9 (1978), 59-70. (1978) MR0500832
  8. Engelking R., General Topology, Polish Scientific Publishers Warsaw (1977). (1977) Zbl0373.54002MR0500780
  9. Gillman L., Jerison M., Rings of continuous functions, Van Nostrand Princeton (1960). (1960) Zbl0093.30001MR0116199
  10. Guthrie J.A., Stone H.E., Pseudocompactness and invariance of continuity, Gen. Top. Applic. 7 (1977), 1-13. (1977) Zbl0345.54017MR0442872
  11. Hechler S.H., Two 𝐑 -closed spaces revisited, Proc. Amer. Math. Soc. 56 (1976), 303-309. (1976) MR0405354
  12. Herrlich H., T υ -Abgeschlossenheit and T υ -Minimalität, Math. Zeit. 88 (1965), 285-294. (1965) MR0184191
  13. Hodel R., Cardinal functions I, Handbook of Set-theoretic Topology, Kunen, Vaughan North-Holland, Amsterdam (1984), 1-61. (1984) MR0776620
  14. Mandelker M., Supports of continuous functions, Trans. Amer. Math. Soc. 156 (1971), 73-83. (1971) Zbl0197.48703MR0275367
  15. Porter J.R., Stephenson R.M., Jr., and Woods R.G., Maximal feebly compact spaces, Topology Applic. to appear. 
  16. Porter J.R., Stephenson R.M., Jr., and Woods R.G., Spaces with maximal feebly compact expansions, preprint. 
  17. Porter J.R., Vermeer J., Spaces with coarser minimal Hausdorff topologies, Trans. Amer. Math. Soc. 289 (1985), 59-71. (1985) Zbl0577.54019MR0779052
  18. Porter J.R., Woods R.G., Extensions and Absolutes of Hausdorff spaces, Springer-Verlag New York (1988). (1988) Zbl0652.54016MR0918341
  19. Raha A.B., Maximal topologies, J. Austral. Math. Soc. 15 (1973), 279-290. (1973) Zbl0267.54018MR0324646
  20. Stephenson R.M., Jr., Pseudocompact spaces, Trans. Amer. Math. Soc. 134 (1968), 437-448. (1968) Zbl0169.53903MR0232349
  21. Stephenson R.M., Jr., Minimal first countable topologies, Trans. Amer. Math. Soc. 138 (1969), 115-127. (1969) Zbl0175.19702MR0238261
  22. Stephenson R.M., Jr., Two 𝐑 -closed spaces, Canad. J. Math. 24 (1972), 286-292. (1972) MR0298613
  23. Weston J.D., On the comparison of topologies, J. Lond. Math. Soc. 37 (1957), 342-354. (1957) Zbl0078.36002MR0094776

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