Compacta are maximally -resolvable
István Juhász; Zoltán Szentmiklóssy
Commentationes Mathematicae Universitatis Carolinae (2013)
- Volume: 54, Issue: 2, page 259-261
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topJuhász, István, and Szentmiklóssy, Zoltán. "Compacta are maximally $G_\delta $-resolvable." Commentationes Mathematicae Universitatis Carolinae 54.2 (2013): 259-261. <http://eudml.org/doc/252556>.
@article{Juhász2013,
abstract = {It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $\Delta (X)$ many pairwise disjoint dense subsets, where $\Delta (X)$ denotes the minimum size of a non-empty open set in $X$. The aim of this note is to prove the following analogous result: Every compactum $X$ contains $\Delta _\delta (X)$ many pairwise disjoint $G_\delta $-dense subsets, where $\Delta _\delta (X)$ denotes the minimum size of a non-empty $G_\delta $ set in $X$.},
author = {Juhász, István, Szentmiklóssy, Zoltán},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact spaces; $G_\delta $-sets; resolvability; compact space; resolvable space; maximally resolvable space; -set},
language = {eng},
number = {2},
pages = {259-261},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Compacta are maximally $G_\delta $-resolvable},
url = {http://eudml.org/doc/252556},
volume = {54},
year = {2013},
}
TY - JOUR
AU - Juhász, István
AU - Szentmiklóssy, Zoltán
TI - Compacta are maximally $G_\delta $-resolvable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 2
SP - 259
EP - 261
AB - It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $\Delta (X)$ many pairwise disjoint dense subsets, where $\Delta (X)$ denotes the minimum size of a non-empty open set in $X$. The aim of this note is to prove the following analogous result: Every compactum $X$ contains $\Delta _\delta (X)$ many pairwise disjoint $G_\delta $-dense subsets, where $\Delta _\delta (X)$ denotes the minimum size of a non-empty $G_\delta $ set in $X$.
LA - eng
KW - compact spaces; $G_\delta $-sets; resolvability; compact space; resolvable space; maximally resolvable space; -set
UR - http://eudml.org/doc/252556
ER -
References
top- Čech E., Pospíšil B., Sur les espaces compacts, Publ. Fac. Sci. Univ. Masaryk 258 (1938), 1–14. Zbl0019.08903
- Comfort W.W., Garcia-Ferreira S., 10.1016/S0166-8641(96)00052-1, Topology Appl. 74 (1996), 149–167. Zbl0866.54004MR1425934DOI10.1016/S0166-8641(96)00052-1
- El'kin A.G., Resolvable spaces which are not maximally resolvable, Vestnik Moskov. Univ. Ser. I Mat. Meh. 24 (1969), no. 4, 66–70. Zbl0243.54018MR0256331
- Juhász I., Cardinal functions in topology – 10 years later, Mathematical Centre Tracts, 123, Mathematisch Centrum, Amsterdam, 1980.
- Juhász I., On the minimum character of points in compact spaces, in: Proc. Top. Conf. (Pécs, 1989), 365–371, Colloq. Math. Soc. János Bolyai, 55, North-Holland, Amsterdam, 1993. Zbl0798.54005MR1244377
- Juhász I., Szentmiklóssy Z., 10.2307/2159502, Proc. Amer. Math. Soc. 116 (1992), 1153–1160. Zbl0767.54002MR1137223DOI10.2307/2159502
NotesEmbed ?
topYou 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.