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Title: Pseudouniform topologies on $C(X)$ given by ideals (English)
Author: Pichardo-Mendoza, Roberto
Author: Tamariz-Mascarúa, Ángel
Author: Villegas-Rodríguez, Humberto
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 54
Issue: 4
Year: 2013
Pages: 557-577
Summary lang: English
Category: math
Summary: Given a Tychonoff space $X$, a base $\alpha$ for an ideal on $X$ is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on $\alpha$ converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space. (English)
Keyword: function space
Keyword: topology of uniform convergence
Keyword: ideal
Keyword: uniformity
Keyword: Lindelöf property
Keyword: pseudouniform ideal
Keyword: almost pseudo-$\omega$-bounded
MSC: 54A10
MSC: 54A20
MSC: 54A25
MSC: 54C35
MSC: 54D20
MSC: 54E15
idZBL: Zbl 06373983
idMR: MR3125075
Date available: 2013-10-01T21:19:06Z
Last updated: 2016-01-04
Stable URL:
Reference: [1] Arkhangel'skii A.V.: Topological Function Spaces.Mathematics and its Applications, 78, Kluwer Academic Publishers, Dordrecht, 1992 (translated from the Russian). MR 1144519
Reference: [2] Engelking R.: General Topology.second edition, Sigma Series in Pure Mathematics, 6, Heldermann Verlag, Berlin, 1989; translated from the Polish by the author; MR 91c:54001. Zbl 0684.54001, MR 1039321
Reference: [3] Gul'ko S.P.: On properties of subsets of $\Sigma$-products.Soviet Math. Dokl. 18 (1977), 1438–1442.
Reference: [4] Isiwata T.: On convergences of sequences of continuous functions.Proc. Japan Acad. 37 (1961), no. 1, 4–9. Zbl 0102.32201, MR 0141069
Reference: [5] Jech T.: Set Theory.The Third Milleniun Edition, revised and expanded, Springer Monographs in Mathematics, 3rd rev. ed. Corr. 4th printing, Springer, Berlin, 2003. Zbl 1007.03002, MR 1940513
Reference: [6] Kundu S., McCoy R.A.: Topologies between compact and uniform convergence on function spaces.Internat. J. Math. Math. Sci. 16 (1993), no. 1, 101–109. Zbl 0798.54020, MR 1200117, 10.1155/S0161171293000122
Reference: [7] Kunen K.: Set Theory. An Introduction to Independence Proofs.Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing Co., Amsterdam, 1980. Zbl 0534.03026, MR 0597342
Reference: [8] McCoy R.A., Ntantu I.: Topological properties of spaces of continuous functions.Lecture Notes in Mathematics, 1315, Springer, Berlin, 1988. Zbl 0647.54001, MR 0953314
Reference: [9] Shakhmatov D.B.: A pseudocompact Tychonoff space all countable subsets of which are closed and $C^*$-embedded.Topology Appl. 22 (1986), no. 2, 139–144. MR 0836321, 10.1016/0166-8641(86)90004-0
Reference: [10] Todorčević S.: Trees and linearly ordered sets.Handbook of Set-Theoretic Topology, (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 235–293. Zbl 0557.54021, MR 0776625
Reference: [11] Turzanski M.: On generalizations of dyadic Frolík Z. (ed.), Proceedings of the 17th Winter School on Abstract Analysis. Charles University, Praha, 1989, pp. 153–159. Zbl 0713.54040, MR 1046462
Reference: [12] Vaughan J.E.: Countably compact and sequentially compact spaces.Handbook of Set-Theoretic Topology, (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 569–602. Zbl 0562.54031, MR 0776631


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