Displaying similar documents to “Two remarks on weaker connected topologies”

On dense subspaces satisfying stronger separation axioms

Ofelia Teresa Alas, Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson, Ivan V. Yashchenko (2001)

Czechoslovak Mathematical Journal

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We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than c has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight c which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of π -weight less than 𝔭 has a dense completely Hausdorff (and hence Urysohn) subspace....

Remarks on dense subspaces

Eva Murtinová (2004)

Czechoslovak Mathematical Journal

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Some constructions of spaces with/without dense subspaces satisfying stronger separation axioms are presented.

Disconnectedness properties of hyperspaces

Rodrigo Hernández-Gutiérrez, Angel Tamariz-Mascarúa (2011)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a Hausdorff space and let ℋ be one of the hyperspaces C L ( X ) , 𝒦 ( X ) , ℱ ( X ) or ℱ n ( X ) ( n a positive integer) with the Vietoris topology. We study the following disconnectedness properties for ℋ : extremal disconnectedness, being a F ' -space, P -space or weak P -space and hereditary disconnectedness. Our main result states: if X is Hausdorff and F ⊂ X is a closed subset such that (a) both F and X - F are totally disconnected, (b) the quotient X / F is hereditarily disconnected, then 𝒦 ( X ) is hereditarily disconnected....