We prove that every continuum of weight א1 is a continuous image of the Čech-Stone-remainder R∗ of the real line. It follows that under CH the remainder of the half line [0,∞) is universal among the… (More)

An Efimov space is a compact space which contains neither a nontrivial converging sequence nor a copy of the Stone-Cech compactification of the integers. We give a new construction of a space which… (More)

OBJECTIVE
Rapid delivery of migraine-specific medication to its site(s) of action is thought to be crucial in preventing or minimizing sensitization of central pain pathways and thereby in optimizing… (More)

The Lindelöf property of the space of continuous real-valued continuous functions is studied. A consistent example of an uncountable Ψ-like space is constructed for which the space of continuous… (More)

Eric van Douwen [vD93] produced a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of βN. We prove that there are… (More)

Hušek defines a space X to have a small diagonal if each uncountable subset of X disjoint from the diagonal, has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a… (More)

We consider the question of whether a compact space will always have a discrete subset whose closure has the same cardinality as the whole space. We obtain many positive results for compact spaces of… (More)

It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of… (More)