Displaying similar documents to “Locally realcompact and HN-complete spaces”

On the subsets of non locally compact points of ultracomplete spaces

Iwao Yoshioka (2002)

Commentationes Mathematicae Universitatis Carolinae

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In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space X at which X is not locally compact and call it an nlc set. In 1999, Garc’ıa-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved that every ultracomplete GO-space has a compact nlc set. In this paper, ultracomplete spaces...

Čech-completeness and ultracompleteness in “nice spaces”

Miguel López de Luna, Vladimir Vladimirovich Tkachuk (2002)

Commentationes Mathematicae Universitatis Carolinae

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We prove that if X n is a union of n subspaces of pointwise countable type then the space X is of pointwise countable type. If X ω is a countable union of ultracomplete spaces, the space X ω is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2].