A basic approach to the perfect extensions of spaces

Giorgio Nordo

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 3, page 571-580
  • ISSN: 0010-2628

Abstract

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In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S 1 ], [S 2 ], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.

How to cite

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Nordo, Giorgio. "A basic approach to the perfect extensions of spaces." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 571-580. <http://eudml.org/doc/248046>.

@article{Nordo1997,
abstract = {In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S$_1$], [S$_2$], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.},
author = {Nordo, Giorgio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {extension; maximal extension; perfect extension; perfect pair; perfect extension; perfect pair},
language = {eng},
number = {3},
pages = {571-580},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A basic approach to the perfect extensions of spaces},
url = {http://eudml.org/doc/248046},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Nordo, Giorgio
TI - A basic approach to the perfect extensions of spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 571
EP - 580
AB - In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S$_1$], [S$_2$], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.
LA - eng
KW - extension; maximal extension; perfect extension; perfect pair; perfect extension; perfect pair
UR - http://eudml.org/doc/248046
ER -

References

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  1. Diamond B., A characterization of those spaces having zero-dimensional remainders, Rocky Mountain Journal of Math. 15 1 (1985), 47-60. (1985) Zbl0572.54022MR0779251
  2. Engelking R., General Topology, Monografie Matematyczne, Warzawa, 1977. Zbl0684.54001MR0500780
  3. Porter J.R., Woods R.G., Extensions and absolutes of Hausdorff spaces, Springer, 1988. Zbl0652.54016MR0918341
  4. Skljarenko E.G., On perfect bicompact extensions, Dokl. Akad. Nauk SSSR 137 (1961), 39-41 Soviet Math. Dokl. 2 (1961), 238-240. (1961) MR0121777
  5. Skljarenko E.G., Some questions in the theory of bicompactifications, Izv. Akad. Nauk. SSSR, Ser. Mat. 26 (1962), 427-452 Trans. Amer. Math. Soc. 58 (1966), 216-244. (1966) MR0143174

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