On the subsets of non locally compact points of ultracomplete spaces

Iwao Yoshioka

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 4, page 707-721
  • ISSN: 0010-2628

Abstract

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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 which have compact nlc sets are studied. Such spaces contain dense locally compact subspaces and coincide with ultracomplete spaces in the realms of normal γ -spaces or ks-spaces.

How to cite

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Yoshioka, Iwao. "On the subsets of non locally compact points of ultracomplete spaces." Commentationes Mathematicae Universitatis Carolinae 43.4 (2002): 707-721. <http://eudml.org/doc/248984>.

@article{Yoshioka2002,
abstract = {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 compact nlc sets are studied. Such spaces contain dense locally compact subspaces and coincide with ultracomplete spaces in the realms of normal $\gamma $-spaces or ks-spaces.},
author = {Yoshioka, Iwao},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally compact; ultracomplete; Čech-complete; countable character; bounded set; locally compact; ultracomplete; Čech-complete},
language = {eng},
number = {4},
pages = {707-721},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the subsets of non locally compact points of ultracomplete spaces},
url = {http://eudml.org/doc/248984},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Yoshioka, Iwao
TI - On the subsets of non locally compact points of ultracomplete spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 4
SP - 707
EP - 721
AB - 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 compact nlc sets are studied. Such spaces contain dense locally compact subspaces and coincide with ultracomplete spaces in the realms of normal $\gamma $-spaces or ks-spaces.
LA - eng
KW - locally compact; ultracomplete; Čech-complete; countable character; bounded set; locally compact; ultracomplete; Čech-complete
UR - http://eudml.org/doc/248984
ER -

References

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  15. Yoshioka I., On the metrizations of γ -spaces and ks-spaces, Questions Answers Gen. Topology 19 (2001), 55-72. (2001) Zbl0983.54030MR1815346

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