Pseudouniform topologies on C ( X ) given by ideals

Roberto Pichardo-Mendoza; Angel Tamariz-Mascarúa; Humberto Villegas-Rodríguez

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 4, page 557-577
  • ISSN: 0010-2628

Abstract

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Given a Tychonoff space X , a base α 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 α 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.

How to cite

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Pichardo-Mendoza, Roberto, Tamariz-Mascarúa, Angel, and Villegas-Rodríguez, Humberto. "Pseudouniform topologies on $C(X)$ given by ideals." Commentationes Mathematicae Universitatis Carolinae 54.4 (2013): 557-577. <http://eudml.org/doc/260696>.

@article{Pichardo2013,
abstract = {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.},
author = {Pichardo-Mendoza, Roberto, Tamariz-Mascarúa, Angel, Villegas-Rodríguez, Humberto},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {function space; topology of uniform convergence; ideal; uniformity; Lindelöf property; pseudouniform ideal; almost pseudo-$\omega $-bounded; function space; topology of uniform convergence; ideal; uniformity; Lindelöf property; pseudouniform ideal; almost pseudo--bounded},
language = {eng},
number = {4},
pages = {557-577},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Pseudouniform topologies on $C(X)$ given by ideals},
url = {http://eudml.org/doc/260696},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Pichardo-Mendoza, Roberto
AU - Tamariz-Mascarúa, Angel
AU - Villegas-Rodríguez, Humberto
TI - Pseudouniform topologies on $C(X)$ given by ideals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 4
SP - 557
EP - 577
AB - 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.
LA - eng
KW - function space; topology of uniform convergence; ideal; uniformity; Lindelöf property; pseudouniform ideal; almost pseudo-$\omega $-bounded; function space; topology of uniform convergence; ideal; uniformity; Lindelöf property; pseudouniform ideal; almost pseudo--bounded
UR - http://eudml.org/doc/260696
ER -

References

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  9. Shakhmatov D.B., 10.1016/0166-8641(86)90004-0, Topology Appl. 22 (1986), no. 2, 139–144. MR0836321DOI10.1016/0166-8641(86)90004-0
  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. Zbl0557.54021MR0776625
  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. Zbl0713.54040MR1046462
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