Perfect compactifications of functions

Giorgio Nordo; Boris A. Pasynkov

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 3, page 619-629
  • ISSN: 0010-2628

Abstract

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We prove that the maximal Hausdorff compactification χ f of a T 2 -compactifiable mapping f and the maximal Tychonoff compactification β f of a Tychonoff mapping f (see [P]) are perfect. This allows us to give a characterization of all perfect Hausdorff (respectively, all perfect Tychonoff) compactifications of a T 2 -compactifiable (respectively, of a Tychonoff) mapping, which is a generalization of two results of Skljarenko [S] for the Hausdorff compactifications of Tychonoff spaces.

How to cite

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Nordo, Giorgio, and Pasynkov, Boris A.. "Perfect compactifications of functions." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 619-629. <http://eudml.org/doc/248605>.

@article{Nordo2000,
abstract = {We prove that the maximal Hausdorff compactification $\chi f$ of a $T_2$-compactifiable mapping $f$ and the maximal Tychonoff compactification $\beta f$ of a Tychonoff mapping $f$ (see [P]) are perfect. This allows us to give a characterization of all perfect Hausdorff (respectively, all perfect Tychonoff) compactifications of a $T_2$-compactifiable (respectively, of a Tychonoff) mapping, which is a generalization of two results of Skljarenko [S] for the Hausdorff compactifications of Tychonoff spaces.},
author = {Nordo, Giorgio, Pasynkov, Boris A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hausdorff (Tychonoff) mapping; compactification of a mapping; maximal Hausdorff (Tychonoff) compactification of a mapping; perfect compactification of a mapping; compactification of maps},
language = {eng},
number = {3},
pages = {619-629},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Perfect compactifications of functions},
url = {http://eudml.org/doc/248605},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Nordo, Giorgio
AU - Pasynkov, Boris A.
TI - Perfect compactifications of functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 619
EP - 629
AB - We prove that the maximal Hausdorff compactification $\chi f$ of a $T_2$-compactifiable mapping $f$ and the maximal Tychonoff compactification $\beta f$ of a Tychonoff mapping $f$ (see [P]) are perfect. This allows us to give a characterization of all perfect Hausdorff (respectively, all perfect Tychonoff) compactifications of a $T_2$-compactifiable (respectively, of a Tychonoff) mapping, which is a generalization of two results of Skljarenko [S] for the Hausdorff compactifications of Tychonoff spaces.
LA - eng
KW - Hausdorff (Tychonoff) mapping; compactification of a mapping; maximal Hausdorff (Tychonoff) compactification of a mapping; perfect compactification of a mapping; compactification of maps
UR - http://eudml.org/doc/248605
ER -

References

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  8. Nordo G., A basic approach to the perfect extensions of spaces, Comment. Math. Univ. Carolinae 38.3 (1997), 571-580. (1997) Zbl0937.54014MR1485078
  9. Norin V.P., On proximities for mappings, Vestn. Mosk. Univ. Math. Mech. Ser. I 1982, no. 4 (1982), 33-36; Moscow Univ. Math. Bull. 37, no. 4 (1982), 40-44. Zbl0508.54023MR0671884
  10. Pasynkov B.A., On extension to mappings of certain notions and assertions concerning spaces, in: Mapping and Functors, Izdat. MGU, Moscow, 1984, pp.72-102 (in Russian). MR0791256
  11. Skljarenko E.G., On perfect bicompact extensions, Dokl. Akad. Nauk SSSR 137 (1961), 39-41; English transl.: Soviet Math. Dokl. 2 (1961), 238-240. (1961) MR0121777
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