Selections on -spaces
Michael Hrušák; Paul J. Szeptycki; Artur Hideyuki Tomita
Commentationes Mathematicae Universitatis Carolinae (2001)
- Volume: 42, Issue: 4, page 763-769
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topHrušák, Michael, Szeptycki, Paul J., and Tomita, Artur Hideyuki. "Selections on $\Psi $-spaces." Commentationes Mathematicae Universitatis Carolinae 42.4 (2001): 763-769. <http://eudml.org/doc/248769>.
@article{Hrušák2001,
abstract = {We show that if $\mathcal \{A\}$ is an uncountable AD (almost disjoint) family of subsets of $\omega $ then the space $\Psi (\mathcal \{A\})$ does not admit a continuous selection; moreover, if $\mathcal \{A\}$ is maximal then $\Psi (\mathcal \{A\})$ does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.},
author = {Hrušák, Michael, Szeptycki, Paul J., Tomita, Artur Hideyuki},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {MAD family; Vietoris topology; continuous selection; MAD family; Vietoris topology; continuous selection},
language = {eng},
number = {4},
pages = {763-769},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Selections on $\Psi $-spaces},
url = {http://eudml.org/doc/248769},
volume = {42},
year = {2001},
}
TY - JOUR
AU - Hrušák, Michael
AU - Szeptycki, Paul J.
AU - Tomita, Artur Hideyuki
TI - Selections on $\Psi $-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 4
SP - 763
EP - 769
AB - We show that if $\mathcal {A}$ is an uncountable AD (almost disjoint) family of subsets of $\omega $ then the space $\Psi (\mathcal {A})$ does not admit a continuous selection; moreover, if $\mathcal {A}$ is maximal then $\Psi (\mathcal {A})$ does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.
LA - eng
KW - MAD family; Vietoris topology; continuous selection; MAD family; Vietoris topology; continuous selection
UR - http://eudml.org/doc/248769
ER -
References
top- G. Artico, U. Marconi, J. Pelant, L. Rotter and M. Tkachenko, Selections and suborderability, preprint. MR1971236
- Balcar B., Dočkálková J., Simon P., Almost disjoint families of countable sets, Colloq. Math. Soc. János Bolyai, Finite and Infinite Sets 37 59-88 (1984). (1984) MR0818228
- van Douwen E.K., Mappings from hyperspaces and convergent sequences, Topology Appl. 34 35-45 (1990). (1990) Zbl0715.54004MR1035458
- van Douwen E., The integers and topology, in K. Kunen, J. Vaughn, editors, Handbook of Set Theoretic Topology 111-167 North-Holland (1984). (1984) Zbl0561.54004MR0776622
- Kunen K., Set Theory: An Introduction to Independence Proofs, North-Holland Amsterdam (1980). (1980) Zbl0443.03021MR0597342
- Mathias A.R.D., Happy families, Ann. Math. Logic 12 59-111 (1977). (1977) Zbl0369.02041MR0491197
- van Mill J., Wattel E., Selections and orderability, Proc. Amer. Math. Soc. 83 601-605 (1981). (1981) Zbl0473.54010MR0627702
- Michael E., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 152-182 (1951). (1951) Zbl0043.37902MR0042109
- Mrówka S., Some set-theoretic constructions in topology, Fund. Math. 94 83-92 (1977). (1977) MR0433388
- Simon P., A compact Fréchet space whose square is not Fréchet, Comment. Math. Univ. Carolinae 21 749-753 (1980). (1980) Zbl0466.54022MR0597764
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.