Showing papers on "Transfinite induction published in 1976"
TL;DR: In this paper, a compactT2 spaceX which is separable, scattered and uncountable, but still so that Xα−Xα+1is countable for all α∈[1, ω] is constructed.
Abstract: A compactT2 spaceX which is separable, scattered and uncountable, but still so thatXα−Xα+1is countable for all α∈[1, ω) is constructed. This answers one of the problems presented by M. E. Rudin in a conference as an open problem and attributed by her to Telgarsky.
22 citations
1 Jan 1976
8 citations
TL;DR: In this paper, it was shown that among set systems consisting of infinite sets, the second proper ty implies the first one, and that this is no longer true for set systems containing finite sets.
Abstract: A set system 9/is said to have the transversal property if there is a oneto-one choice function on 9/. The aim of this paper is to prove, answering a question of A. HAJN~L, that among set systems consisting of infinite sets the second proper ty implies the first one. Easy examples show that this is no longer t rue for set systems containing finite sets. We will make use of the following well-known lemma of BmLNSTmN [1].
7 citations
Journal Article•
1 citations