Strong shape of the Stone-Čech compactification

Sibe Mardešić

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 533-539
  • ISSN: 0010-2628

Abstract

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J. Keesling has shown that for connected spaces X the natural inclusion e : X → β X of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.

How to cite

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Mardešić, Sibe. "Strong shape of the Stone-Čech compactification." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 533-539. <http://eudml.org/doc/247416>.

@article{Mardešić1992,
abstract = {J. Keesling has shown that for connected spaces $X$ the natural inclusion $e:X\rightarrow \beta X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.},
author = {Mardešić, Sibe},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {inverse system; resolution; Stone-Čech compactification; pseudocompact space; shape; strong shape; pseudocompact space; Stone-Čech compactification; strong shape},
language = {eng},
number = {3},
pages = {533-539},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Strong shape of the Stone-Čech compactification},
url = {http://eudml.org/doc/247416},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Mardešić, Sibe
TI - Strong shape of the Stone-Čech compactification
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 533
EP - 539
AB - J. Keesling has shown that for connected spaces $X$ the natural inclusion $e:X\rightarrow \beta X$ of $X$ in its Stone-Čech compactification is a shape equivalence if and only if $X$ is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.
LA - eng
KW - inverse system; resolution; Stone-Čech compactification; pseudocompact space; shape; strong shape; pseudocompact space; Stone-Čech compactification; strong shape
UR - http://eudml.org/doc/247416
ER -

References

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  1. Dowker C.H., Mapping theorems for noncompact spaces, Amer. J. Math. 69 (1947), 200-240. (1947) MR0020771
  2. Engelking R., General Topology, Polish Sci. Publ., Warsaw, 1977. Zbl0684.54001MR0500780
  3. Glicksberg I., Stone-Čech compactifications of products, Trans. Amer. Math. Soc. 90 (1959), 369-382. (1959) Zbl0089.38702MR0105667
  4. Keesling J., Shape theory and the Stone-Čech compactification, in Proc. Internat. Conference on Geometric Topology, Polish Sci. Publ., Warsaw, 1980, pp. 236-243. Zbl0477.54018MR0656750
  5. Keesling K., Sher R.B., Shape properties of the Stone-Čech compactification, General Topology and Appl. 9 (1978), 1-8. (1978) Zbl0396.54018MR0478105
  6. Lisica Ju.T., Mardešić S., Coherent prohomotopy and a strong shape category of topological spaces, in Proc. Internat. Topological Conference (Leningrad 1982), Lecture Notes in Math. 1060, Springer-Verlag, Berlin, 1984, pp. 164-173. MR0770236
  7. Lisica Ju.T., Mardešić S., Coherent prohomotopy and strong shape theory, Glasnik Mat. 19 (39) (1984), 335-399. (1984) MR0790021
  8. Lončar I., Some results on resolution of spaces, Rad Jugoslav. Akad. Znan. Umjetn. Matem. Znan. 428 (6) (1987), 37-49. (1987) MR0960457
  9. Mardešić S., Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114 (1981), 53-78. (1981) MR0643305
  10. Mardešić S., Segal J., Shape Theory, North-Holland, Amsterdam, 1982. MR0676973
  11. Morita K., On shapes of topological spaces, Fund. Math. 86 (1975), 251-259. (1975) Zbl0296.54034MR0388385
  12. Walker R.C., The Stone-Čech compactification, Springer-Verlag, Berlin, 1974. Zbl0292.54001MR0380698

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