Selections on Ψ -spaces

Michael Hrušák; Paul J. Szeptycki; Artur Hideyuki Tomita

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 4, page 763-769
  • ISSN: 0010-2628

Abstract

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We show that if 𝒜 is an uncountable AD (almost disjoint) family of subsets of ω then the space Ψ ( 𝒜 ) does not admit a continuous selection; moreover, if 𝒜 is maximal then Ψ ( 𝒜 ) does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.

How to cite

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Hrušák, 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

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