Some results on sequentially compact extensions
Vipera, Maria Cristina
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 819-831 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1998-01-01
Classification:  54C20,  54D35,  54D80 
@article{119056,
     author = {Maria Cristina Vipera},
     title = {Some results on sequentially compact extensions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {819-831},
     zbl = {1060.54507},
     mrnumber = {1715470},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119056}
}

Vipera, Maria Cristina. Some results on sequentially compact extensions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 819-831. http://gdmltest.u-ga.fr/item/119056/

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) | MR 1154977 | Zbl 0772.54018

Caterino A.; Guazzone S. Extensions of unbounded topological spaces, to appear. | MR 1675263 | Zbl 0977.54021

Van Douwen E.K. The integers and topology, in Handbook of Set Theoretic Topology, North Holland, 1984. | MR 0776622 | Zbl 0561.54004

Engelking R. General Topology, Heldermann, Berlin, 1989. | MR 1039321 | Zbl 0684.54001

Faulkner G.D.; Vipera M.C. Sequentially compact extensions, Questions Answers Gen. Topology 14 (1996), 196-207. (1996) | MR 1403345 | Zbl 0865.54021

Gillman L.; Jerison M. Rings of Continuous functions, Van Nostrand, 1960. | MR 0116199 | Zbl 0327.46040

Hu S.-T. Boundedness in a topological space, J. Math. Pures Appl. 28 (1949), 287-320. (1949) | MR 0033527 | Zbl 0041.31602

Juhász I. Variation on tightness, Studia Sci. Math. Hungar. 24 (1989), 58-61. (1989)

Kato A. Various countably-compact-ifications and their applications, Gen. Top. Appl. 8 (1978), 27-46. (1978) | MR 0464167 | Zbl 0372.54025

Loeb P.A. A minimal compactification for extending continuous functions, Proc. Amer. Math. Soc. 18 (1967), 282-283. (1967) | MR 0216468 | Zbl 0146.44503

Morita K. Countably-compactifiable spaces, Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A 12 (1973), 7-15. (1973) | MR 0370507 | Zbl 0277.54024

Nogura N. Countably compact extensions of topological spaces, Topology Appl. 15 (1983), 65-69. (1983) | MR 0676967 | Zbl 0496.54021

Nyikos P.J.; Vaughan J.E. The Scarborough-Stone problem for Hausdorff spaces, Topology Appl. 44 (1992), 309-316. (1992) | MR 1173267 | Zbl 0758.54010

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. | MR 1346339

Tkachuk V.V. Almost Lindelöf and locally Lindelöf spaces, Izvestiya VUZ Matematika 32 (1988), 84-88. (1988) | MR 0941256 | Zbl 0666.54014

Vaughan J.E. Countably compact and sequentially compact spaces, in Handbook of Set Theoretic Topology, North Holland, 1984. | MR 0776631 | Zbl 0562.54031

Whyburn G.T. A unified space for mappings, Trans. Amer. Math. Soc. 74 (1953), 344-350. (1953) | MR 0052762 | Zbl 0053.12303