We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X)… (More)

We obtain several results and examples concerning the general question “When must a space with a small diagonal have a Gδ-diagonal?”. In particular, we show (1) every compact metrizably fibered space… (More)

In this note we show that quotients of countably based spaces (qcb spaces) and topological predomains as introduced by M. Schröder and A. Simpson are not closed under sobrification. As a consequence… (More)

We answer a question of Alas, Tkacenko, Tkachuk, and Wilson by constructing a metrizable space with no compact open subsets which cannot be densely embedded in a connected metrizable (or even… (More)

A sharp base B is a base such that whenever (Bi)i<ω is an injective sequence from B with x ∈ i<ω Bi, then { ⋂ i<n Bi : n < ω} is a base at x. Alleche, Arhangel’skĭı and Calbrix asked: if X has a… (More)

Under the assumption that the real line cannot be covered by ω1-many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into ω1-many closed nowhere dense sets; (b) no… (More)

The notions of thin and very thin dense subsets of a product space were introduced by the third author, and in this article we also introduce the notion of a slim dense set in a product. We obtain a… (More)

In the author’s dissertation, he introduced a simple topological game. Seemingly minor variations of this game have over the years seen various uses, including the characterization of Corson and… (More)

A space X is a D-space if whenever one is given a neighborhood N(x) of x for each x ∈ X, then there is a closed discrete subset D of X such that {N(x) : x ∈ D} covers X. It is a decades-old open… (More)

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider… (More)