A generalization of boundedly compact metric spaces

Gerald Beer; Anna Di Concilio

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 361-367
  • ISSN: 0010-2628

Abstract

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A metric space 〈 X , d 〉 is called a UC space provided each continuous function on X into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that UC spaces play relative to the compact metric spaces.

How to cite

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Beer, Gerald, and Di Concilio, Anna. "A generalization of boundedly compact metric spaces." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 361-367. <http://eudml.org/doc/247275>.

@article{Beer1991,
abstract = {A metric space $\langle X,d\rangle $ is called a $\operatorname\{UC\}$ space provided each continuous function on $X$ into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that $\operatorname\{UC\}$ spaces play relative to the compact metric spaces.},
author = {Beer, Gerald, Di Concilio, Anna},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\operatorname\{UC\}$ space; boundedly $\operatorname\{UC\}$ space; boundedly compact space; Atsuji space; uniform continuity on bounded sets; topology of uniform convergence on bounded sets; Attouch–Wets topology; UC spaces; boundedly compact spaces; set of nonisolated points; Hausdorff metric; Attouch-Wets topology},
language = {eng},
number = {2},
pages = {361-367},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A generalization of boundedly compact metric spaces},
url = {http://eudml.org/doc/247275},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Beer, Gerald
AU - Di Concilio, Anna
TI - A generalization of boundedly compact metric spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 361
EP - 367
AB - A metric space $\langle X,d\rangle $ is called a $\operatorname{UC}$ space provided each continuous function on $X$ into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that $\operatorname{UC}$ spaces play relative to the compact metric spaces.
LA - eng
KW - $\operatorname{UC}$ space; boundedly $\operatorname{UC}$ space; boundedly compact space; Atsuji space; uniform continuity on bounded sets; topology of uniform convergence on bounded sets; Attouch–Wets topology; UC spaces; boundedly compact spaces; set of nonisolated points; Hausdorff metric; Attouch-Wets topology
UR - http://eudml.org/doc/247275
ER -

References

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