D-spaces and dually discrete spaces
by
Richard G. Wilson
Universidad Autónoma Metropolitana, Unidad Iztapalapa
Coauthors: Ofelia T. Alas, Vladimir V. Tkachuk

A neighbourhood assignment in a space X is a family O={O_x:x ∈ X} of open subsets of X such that x ∈ O_x for any x ∈ X. A set Y ⊆ X is a kernel of O if O(Y)=∪{O_x:x ∈ Y}=X. If every neighbourhood assignment in X has a closed and discrete (respectively, discrete) kernel, then X is said to be a D-space (respectively, a dually discrete space). We will discuss some new results concerning D-spaces and dually discrete spaces. Among other results, we show that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf P-space is a D-space and we prove an addition theorem for metalindelöf spaces which answers a question of Arhangel'skii and Buzyakova.

Date received: May 14, 2008