Displaying similar documents to “Remote points in β R ”

Property ( a ) and dominating families

Samuel Gomes da Silva (2005)

Commentationes Mathematicae Universitatis Carolinae

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Generalizations of earlier negative results on Property ( a ) are proved and two questions on an ( a ) -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ 2 ω is regular” and “ 2 ω < 2 ω 1 ” the existence of a T 1 separable locally compact ( a ) -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal...

Lonely points revisited

Jonathan L. Verner (2013)

Commentationes Mathematicae Universitatis Carolinae

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In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point p ∈ X is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space 𝒢 ω from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745–748] to construct lonely points in ω * . This answers the question...

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....