Examples from trees, related to discrete subsets, pseudo-radiality and \(\omega \)-boundedness (Q1005172)

Discrete subspaces have been shown to be subspaces that can say much about the whole space. For example, discretely reflexive properties and discretely generated properties have been discussed in the past few years. In this paper the author presents some constructions using trees, mainly Souslin trees, that give counterexamples for the discrete reflection of certain topological properties. Also, assuming the existence of a Souslin tree, a compact space that is pseudo-radial but not discretely generated is constructed. A first-countable space that is \(\omega\)-bounded but not strongly \(\omega\)-bounded is given using an Aronszajn tree.