D-spaces

Mirna Dzamonja

Let X be a topological space, and τ its topology. An open neigbourhood assignmenet ONA on X is a function assigning to each x in X a member of τ that contains x. A topological space is called a D space if for every ONA U of X there is a closed discrete subspace D of X such that {U(x) : xinD} = X. We show that it is consistent that every locally countable space X of size ≤ ℵ_{2} in which every open subspace of size ≤ ℵ_{1} is strongly D, is D itself.

Address: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

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