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On the subsets of non locally compact points of ultracomplete spaces

Iwao Yoshioka (2002)

Commentationes Mathematicae Universitatis Carolinae

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 which have...

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