Tightness and resolvability

Angelo Bella; Viacheslav I. Malykhin

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 177-184
  • ISSN: 0010-2628

Abstract

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We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.

How to cite

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Bella, Angelo, and Malykhin, Viacheslav I.. "Tightness and resolvability." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 177-184. <http://eudml.org/doc/248252>.

@article{Bella1998,
abstract = {We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.},
author = {Bella, Angelo, Malykhin, Viacheslav I.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {resolvability; maximal resolvability; countable fan-tightness; weakly Fr' echet-Urysohn property; empty interior tightness; disjoint tightness; resolvable space; maximally resolvable space},
language = {eng},
number = {1},
pages = {177-184},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Tightness and resolvability},
url = {http://eudml.org/doc/248252},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Bella, Angelo
AU - Malykhin, Viacheslav I.
TI - Tightness and resolvability
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 177
EP - 184
AB - We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.
LA - eng
KW - resolvability; maximal resolvability; countable fan-tightness; weakly Fr' echet-Urysohn property; empty interior tightness; disjoint tightness; resolvable space; maximally resolvable space
UR - http://eudml.org/doc/248252
ER -

References

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  1. Arhangel'skiĭ A.V., Hurewicz spaces, analytic sets and fan-tightness of spaces of functions, Soviet Math. Dokl. 33 (1986), 396-399. (1986) MR0119188
  2. Arhangel'skiĭA.V., Bella A., Countable fan-tightness versus countable tightness, Comment. Math. Univ. Carolinae 37 3(1996), 565-576. (1996) Zbl0881.54005MR1426921
  3. Comfort W.W., García-Ferreira S., Resolvability: a selective survey and some new results, Topology Appl. 74 (1996), 1-19. (1996) MR1425934
  4. van Douwen E.K., Applications of maximal topologies, Topology Appl. 51 (1993), 125-139. (1993) Zbl0845.54028MR1229708
  5. Hewitt E., A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309-333. (1943) Zbl0060.39407MR0008692
  6. Malykhin V.I., Tironi G., Weakly Fréchet-Urysohn spaces, preprint. 
  7. Pytke'ev E.G., On maximally resolvable spaces, Proc. Steklov Institute of Mathematics (1984), 154 225-230. (1984) 
  8. Sharma P.L., Sharma S., Resolution properties in generalized k -spaces, Topology Appl. 29 (1989), 61-66. (1989) MR0944069

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