M. Hru\v s\' ak, P.J. Szeptycki, A.H. Tomita
Selections on $\Psi $-spaces

Comment.Math.Univ.Carolinae 42,4 (2001) 763-769.

Abstract: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.

Keywords: MAD family, Vietoris topology, continuous selection
AMS Subject Classification: 54C65, 54B20, 03E05