The sup = max problem for the extent of generalized metric spaces

Yasushi Hirata; Yukinobu Yajima

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 2, page 245-257
  • ISSN: 0010-2628

Abstract

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It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.

How to cite

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Hirata, Yasushi, and Yajima, Yukinobu. "The sup = max problem for the extent of generalized metric spaces." Commentationes Mathematicae Universitatis Carolinae 54.2 (2013): 245-257. <http://eudml.org/doc/252490>.

@article{Hirata2013,
abstract = {It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.},
author = {Hirata, Yasushi, Yajima, Yukinobu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {extent; Lindelöf degree; $\Sigma $-space; strict $p$-space; semi-stratifiable; extent; Lindelöf degree; -space; strict -space; semi-stratifiable},
language = {eng},
number = {2},
pages = {245-257},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The sup = max problem for the extent of generalized metric spaces},
url = {http://eudml.org/doc/252490},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Hirata, Yasushi
AU - Yajima, Yukinobu
TI - The sup = max problem for the extent of generalized metric spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 2
SP - 245
EP - 257
AB - It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.
LA - eng
KW - extent; Lindelöf degree; $\Sigma $-space; strict $p$-space; semi-stratifiable; extent; Lindelöf degree; -space; strict -space; semi-stratifiable
UR - http://eudml.org/doc/252490
ER -

References

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