Spaces not distinguishing convergences

Miroslav Repický

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 829-842
  • ISSN: 0010-2628

Abstract

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In the present paper we introduce a convergence condition ( Σ ' ) and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.

How to cite

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Repický, Miroslav. "Spaces not distinguishing convergences." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 829-842. <http://eudml.org/doc/22534>.

@article{Repický2000,
abstract = {In the present paper we introduce a convergence condition $(\Sigma ^\{\prime \})$ and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.},
author = {Repický, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {P-; QN-; $\Sigma $-; $\Sigma ^\{\prime \}$-; $\Sigma ^*$-; $\Sigma _c$-convergence; a space not distinguishing convergences; mQN-space; -space; wQN-space; QN-space; -space QN-space; wQN-space; weak distributivity of a family of sets},
language = {eng},
number = {4},
pages = {829-842},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spaces not distinguishing convergences},
url = {http://eudml.org/doc/22534},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Repický, Miroslav
TI - Spaces not distinguishing convergences
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 829
EP - 842
AB - In the present paper we introduce a convergence condition $(\Sigma ^{\prime })$ and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.
LA - eng
KW - P-; QN-; $\Sigma $-; $\Sigma ^{\prime }$-; $\Sigma ^*$-; $\Sigma _c$-convergence; a space not distinguishing convergences; mQN-space; -space; wQN-space; QN-space; -space QN-space; wQN-space; weak distributivity of a family of sets
UR - http://eudml.org/doc/22534
ER -

References

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  1. Bartoszyński T., Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. (1984) Zbl0538.03042MR0719666
  2. Bukovský L., Recław I., Repický M., Spaces not distinguishing pointwise and quasinormal convergence of real functions, Topology Appl. 41 (1991), 25-40. (1991) Zbl0768.54025MR1129696
  3. Bukovský L., Recław I., Repický M., Spaces not distinguishing convergences of real-valued functions, Topology Appl., to appear. Zbl1067.54028
  4. van Douwen E.K., The integers and topology, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North Holland, Amsterdam, 1984, pp.111-167. Zbl0561.54004MR0776622
  5. Engelking R., General Topology, Państwowe Wydawnictwo Naukowe, Warszawa, 1977. Zbl0684.54001MR0500779
  6. Kada M., Kamo S., New cardinal invariants related to pseudo-Dirichlet sets, preprint, 1996. 
  7. Kuratowski K., Topologie I, PWN, Warsaw, 1958. Zbl0849.01044
  8. Miller A.W., Special subsets of the real line, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North Holland, Amsterdam, 1984, pp.201-233. Zbl0588.54035MR0776624
  9. Recław I., Metric spaces not distinguishing pointwise and quasinormal convergence of real functions, Bull. Polish Acad. Sci. Math. 45 (1997), 3 287-289. (1997) Zbl0897.54013MR1477547

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