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The union of two D-spaces need not be D

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Soukup D., Szeptycki P.

Fundamenta Mathematicae

2013

tom 220

nr 2

129-137

We construct from ⋄ a T₂ example of a hereditarily Lindelöf space X that is not a D-space but is the union of two subspaces both of which are D-spaces. This answers a question of Arhangel'skii.

Wijsman hyperspaces of non-separable metric spaces

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Hernández-Gutiérrez R., Szeptycki P.

Fundamenta Mathematicae

2015

tom 228

nr 1

63-79

Given a metric space ⟨X,ρ⟩, consider its hyperspace of closed sets CL(X) with the Wijsman topology $τ_{W(ρ)}$. It is known that $⟨CL(X),τ_{W(ρ)}⟩$ is metrizable if and only if X is separable, and it is an open question by Di Maio and Meccariello whether this is equivalent to $⟨CL(X),τ_{W(ρ)}⟩$ being normal. We prove that if the weight of X is a regular uncountable cardinal and X is locally separable, then $⟨CL(X),τ_{W(ρ)}⟩$ is not normal. We also solve some questions by Cao, Junnila and Moors regarding isolated points in Wijsman hyperspaces.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Szeptycki P.

1 Hernández-Gutiérrez R.

1 Soukup D.

1 2015

1 2013

Wyniki wyszukiwania

The union of two D-spaces need not be D

Wijsman hyperspaces of non-separable metric spaces