We show that if $\Cal A$ is an uncountable AD (almost disjoint) family of subsets of $\omega$ then the space $\Psi(\Cal A)$ does not admit a continuous selection; moreover, if $\Cal A$ is maximal then $\Psi(\Cal A)$ does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.
@article{119291,
author = {Michael Hru\v s\'ak and Paul J. Szeptycki and Artur Hideyuki Tomita},
title = {Selections on $\Psi$-spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {42},
year = {2001},
pages = {763-769},
zbl = {1090.54506},
mrnumber = {1883384},
language = {en},
url = {http://dml.mathdoc.fr/item/119291}
}
Hrušák, Michael; Szeptycki, Paul J.; Tomita, Artur Hideyuki. Selections on $\Psi$-spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 763-769. http://gdmltest.u-ga.fr/item/119291/
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