Cardinal inequalities implying maximal resolvability

Marek Balcerzak; Tomasz Natkaniec; Małgorzata Terepeta

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 85-91
  • ISSN: 0010-2628

Abstract

top
We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space X is maximally resolvable provided that for a dense set X 0 X and for each x X 0 the π -character of X at x is not greater than the dispersion character of X . On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.

How to cite

top

Balcerzak, Marek, Natkaniec, Tomasz, and Terepeta, Małgorzata. "Cardinal inequalities implying maximal resolvability." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 85-91. <http://eudml.org/doc/249554>.

@article{Balcerzak2005,
abstract = {We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space $X$ is maximally resolvable provided that for a dense set $X_0\subset X$ and for each $x\in X_0$ the $\pi $-character of $X$ at $x$ is not greater than the dispersion character of $X$. On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.},
author = {Balcerzak, Marek, Natkaniec, Tomasz, Terepeta, Małgorzata},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {maximally resolvable space; base at a point; $\pi $-base; $\pi $-character; maximally resolvable space; base at a point; -base},
language = {eng},
number = {1},
pages = {85-91},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Cardinal inequalities implying maximal resolvability},
url = {http://eudml.org/doc/249554},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Balcerzak, Marek
AU - Natkaniec, Tomasz
AU - Terepeta, Małgorzata
TI - Cardinal inequalities implying maximal resolvability
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 85
EP - 91
AB - We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space $X$ is maximally resolvable provided that for a dense set $X_0\subset X$ and for each $x\in X_0$ the $\pi $-character of $X$ at $x$ is not greater than the dispersion character of $X$. On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.
LA - eng
KW - maximally resolvable space; base at a point; $\pi $-base; $\pi $-character; maximally resolvable space; base at a point; -base
UR - http://eudml.org/doc/249554
ER -

References

top
  1. Bella A., The density topology is extraresolvable, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), 495-498. (2000) Zbl1013.54001MR1811549
  2. Bienias J., Terepeta M., A sufficient condition for maximal resolvability of topological spaces, Comment. Math. Univ. Carolinae 45 (2004), 139-144. (2004) Zbl1100.54003MR2076865
  3. Comfort W.W., Garcia-Ferreira S., Resolvability: a selective survey and some new results, Topology Appl. 74 (1996), 149-167. (1996) Zbl0866.54004MR1425934
  4. Engelking R., General Topology, PWN, Warsaw, 1977. Zbl0684.54001MR0500780
  5. Hashimoto H., On the * -topology and its application, Fund. Math. 91 (1976), 5-10. (1976) MR0413058
  6. Hodel R., Cardinals functions I, in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, pp.1-61. MR0776620
  7. Juhasz I., Cardinals functions II, in: Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, pp.63-109. MR0776621
  8. Monk J.D., Appendix on set theory, in: Handbook of Boolean Algebras, vol. 3, Elsevier, Amsterdam, 1989, pp.1215-1233. MR0991617

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.