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 |

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Category: | math |

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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 |

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Date available: | 2013-10-01T21:19:06Z |

Last updated: | 2016-01-04 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/143475 |

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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 spaces.in 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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