Čech-Stone-like compactifications for general topological spaces

Miroslav Hušek

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 1, page 159-163
  • ISSN: 0010-2628

Abstract

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The problem whether every topological space X has a compactification Y such that every continuous mapping f from X into a compact space Z has a continuous extension from Y into Z is answered in the negative. For some spaces X such compactifications exist.

How to cite

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Hušek, Miroslav. "Čech-Stone-like compactifications for general topological spaces." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 159-163. <http://eudml.org/doc/247381>.

@article{Hušek1992,
abstract = {The problem whether every topological space $X$ has a compactification $Y$ such that every continuous mapping $f$ from $X$ into a compact space $Z$ has a continuous extension from $Y$ into $Z$ is answered in the negative. For some spaces $X$ such compactifications exist.},
author = {Hušek, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compactification; mapping-extension; reflection; Wallman remainder; Wallman compactification},
language = {eng},
number = {1},
pages = {159-163},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Čech-Stone-like compactifications for general topological spaces},
url = {http://eudml.org/doc/247381},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Hušek, Miroslav
TI - Čech-Stone-like compactifications for general topological spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 159
EP - 163
AB - The problem whether every topological space $X$ has a compactification $Y$ such that every continuous mapping $f$ from $X$ into a compact space $Z$ has a continuous extension from $Y$ into $Z$ is answered in the negative. For some spaces $X$ such compactifications exist.
LA - eng
KW - compactification; mapping-extension; reflection; Wallman remainder; Wallman compactification
UR - http://eudml.org/doc/247381
ER -

References

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  1. Adámek J., Rosický J., On injectivity classes in locally presented categories, preprint (1991), (to appear in Trans. Amer. Math. Soc). (1991) 
  2. Čech E., Topological spaces, (revised ed. by Z.Frolík, M.Katětov) (Academia Prague 1966). (Academia Prague 1966) MR0211373
  3. Dow A., Watson S., Universal spaces, preprint (December 1990). (December 1990) MR1056167
  4. Engelking R., Topological spaces, Heldermann Verlag Berlin (1990). (1990) 
  5. Giuli E., Hušek M., A diagonal theorem for epireflective subcategories of Top and cowellpoweredness, Ann. di Matem. Pura et Appl. 145 (1986), 337-346. (1986) MR0886716
  6. Giuli E., Simon P., On spaces in which every bounded subset is Hausdorff, Topology and its Appl. 37 (1990), 267-274. (1990) Zbl0719.54009MR1082937
  7. Harris D., The Wallman compactification as a functor, Gen. Top. and its Appl. 1 (1971), 273-281. (1971) Zbl0224.54010MR0292034
  8. Herrlich H., Almost reflective subcategories of Top, preprint (1991) (to appear in Topology and its Appl.). MR1208677
  9. Hušek M., Categorial connections between generalized proximity spaces and compactifications, Contributions to extension theory of topological structures, Proc. Conf. Berlin 1967 (Academia Berlin 1969), 127-132. (Academia Berlin 1969) MR0248730
  10. Hušek M., Remarks on reflections, Comment. Math. Univ. Carolinae 7 (1966), 249-259. (1966) MR0202800

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