Some results on sequentially compact extensions

Maria Cristina Vipera

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 4, page 819-831
  • ISSN: 0010-2628

Abstract

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The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.

How to cite

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Vipera, Maria Cristina. "Some results on sequentially compact extensions." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 819-831. <http://eudml.org/doc/248229>.

@article{Vipera1998,
abstract = {The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.},
author = {Vipera, Maria Cristina},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sequentially compact extension; locally sequentially compact space; extension of functions; sequentially compact extension; locally sequentially compact space; extension of functions},
language = {eng},
number = {4},
pages = {819-831},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some results on sequentially compact extensions},
url = {http://eudml.org/doc/248229},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Vipera, Maria Cristina
TI - Some results on sequentially compact extensions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 4
SP - 819
EP - 831
AB - The class of Hausdorff spaces (or of Tychonoff spaces) which admit a Hausdorff (respectively Tychonoff) sequentially compact extension has not been characterized. We give some new conditions, in particular, we prove that every Tychonoff locally sequentially compact space has a Tychonoff one-point sequentially compact extension. We also give some results about extension of functions and about lattice properties of the family of all minimal sequentially compact extensions of a given space.
LA - eng
KW - sequentially compact extension; locally sequentially compact space; extension of functions; sequentially compact extension; locally sequentially compact space; extension of functions
UR - http://eudml.org/doc/248229
ER -

References

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  1. Caterino A., Faulkner G.D., Vipera M.C., Two applications of singular sets to the theory of compactifications, Rend. Ist. Mat. Univ. Trieste 21 (1989), 248-258. (1989) Zbl0772.54018MR1154977
  2. Caterino A., Guazzone S., Extensions of unbounded topological spaces, to appear. Zbl0977.54021MR1675263
  3. Van Douwen E.K., The integers and topology, in Handbook of Set Theoretic Topology, North Holland, 1984. Zbl0561.54004MR0776622
  4. Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  5. Faulkner G.D., Vipera M.C., Sequentially compact extensions, Questions Answers Gen. Topology 14 (1996), 196-207. (1996) Zbl0865.54021MR1403345
  6. Gillman L., Jerison M., Rings of Continuous functions, Van Nostrand, 1960. Zbl0327.46040MR0116199
  7. Hu S.-T., Boundedness in a topological space, J. Math. Pures Appl. 28 (1949), 287-320. (1949) Zbl0041.31602MR0033527
  8. Juhász I., Variation on tightness, Studia Sci. Math. Hungar. 24 (1989), 58-61. (1989) 
  9. Kato A., Various countably-compact-ifications and their applications, Gen. Top. Appl. 8 (1978), 27-46. (1978) Zbl0372.54025MR0464167
  10. Loeb P.A., A minimal compactification for extending continuous functions, Proc. Amer. Math. Soc. 18 (1967), 282-283. (1967) Zbl0146.44503MR0216468
  11. Morita K., Countably-compactifiable spaces, Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A 12 (1973), 7-15. (1973) Zbl0277.54024MR0370507
  12. Nogura N., Countably compact extensions of topological spaces, Topology Appl. 15 (1983), 65-69. (1983) Zbl0496.54021MR0676967
  13. Nyikos P.J., Vaughan J.E., The Scarborough-Stone problem for Hausdorff spaces, Topology Appl. 44 (1992), 309-316. (1992) Zbl0758.54010MR1173267
  14. Simon P., Product of sequentially compact spaces, Proc. of the Eleventh International Conference of Topology, Trieste 6-11 September, 1993, Rendic. Ist. Mat. Univ. Trieste 25(1-2) (1993), 447-450. MR1346339
  15. Tkachuk V.V., Almost Lindelöf and locally Lindelöf spaces, Izvestiya VUZ Matematika 32 (1988), 84-88. (1988) Zbl0666.54014MR0941256
  16. Vaughan J.E., Countably compact and sequentially compact spaces, in Handbook of Set Theoretic Topology, North Holland, 1984. Zbl0562.54031MR0776631
  17. Whyburn G.T., A unified space for mappings, Trans. Amer. Math. Soc. 74 (1953), 344-350. (1953) Zbl0053.12303MR0052762

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