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Keywords:
sequentially compact extension; locally sequentially compact space; extension of functions
sequentially compact extension; locally sequentially compact space; extension of functions
Summary:
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.
References:
[CFV] 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. MR 1154977 | Zbl 0772.54018
[CG] Caterino A., Guazzone S.: Extensions of unbounded topological spaces. to appear. MR 1675263 | Zbl 0977.54021
[vD] Van Douwen E.K.: The integers and topology. in Handbook of Set Theoretic Topology, North Holland, 1984. MR 0776622 | Zbl 0561.54004
[E] Engelking R.: General Topology. Heldermann, Berlin, 1989. MR 1039321 | Zbl 0684.54001
[FV] Faulkner G.D., Vipera M.C.: Sequentially compact extensions. Questions Answers Gen. Topology 14 (1996), 196-207. MR 1403345 | Zbl 0865.54021
[GJ] Gillman L., Jerison M.: Rings of Continuous functions. Van Nostrand, 1960. MR 0116199 | Zbl 0327.46040
[H] Hu S.-T.: Boundedness in a topological space. J. Math. Pures Appl. 28 (1949), 287-320. MR 0033527 | Zbl 0041.31602
[J] Juhász I.: Variation on tightness. Studia Sci. Math. Hungar. 24 (1989), 58-61.
[K] Kato A.: Various countably-compact-ifications and their applications. Gen. Top. Appl. 8 (1978), 27-46. MR 0464167 | Zbl 0372.54025
[L] Loeb P.A.: A minimal compactification for extending continuous functions. Proc. Amer. Math. Soc. 18 (1967), 282-283. MR 0216468 | Zbl 0146.44503
[M] Morita K.: Countably-compactifiable spaces. Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A 12 (1973), 7-15. MR 0370507 | Zbl 0277.54024
[N] Nogura N.: Countably compact extensions of topological spaces. Topology Appl. 15 (1983), 65-69. MR 0676967 | Zbl 0496.54021
[NV] Nyikos P.J., Vaughan J.E.: The Scarborough-Stone problem for Hausdorff spaces. Topology Appl. 44 (1992), 309-316. MR 1173267 | Zbl 0758.54010
[S] 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
[T] Tkachuk V.V.: Almost Lindelöf and locally Lindelöf spaces. Izvestiya VUZ Matematika 32 (1988), 84-88. MR 0941256 | Zbl 0666.54014
[V] Vaughan J.E.: Countably compact and sequentially compact spaces. in Handbook of Set Theoretic Topology, North Holland, 1984. MR 0776631 | Zbl 0562.54031
[W] Whyburn G.T.: A unified space for mappings. Trans. Amer. Math. Soc. 74 (1953), 344-350. MR 0052762 | Zbl 0053.12303
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