On minimal- α -spaces

Giovanni Lo Faro; Giorgio Nordo; Jack R. Porter

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 4, page 727-740
  • ISSN: 0010-2628

Abstract

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An α -space is a topological space in which the topology is generated by the family of all α -sets (see [N]). In this paper, minimal- α 𝒫 -spaces (where 𝒫 denotes several separation axioms) are investigated. Some new characterizations of α -spaces are also obtained.

How to cite

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Lo Faro, Giovanni, Nordo, Giorgio, and Porter, Jack R.. "On minimal-$\alpha $-spaces." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 727-740. <http://eudml.org/doc/249175>.

@article{LoFaro2003,
abstract = {An $\alpha $-space is a topological space in which the topology is generated by the family of all $\alpha $-sets (see [N]). In this paper, minimal-$\alpha \mathcal \{P\}$-spaces (where $\mathcal \{P\}$ denotes several separation axioms) are investigated. Some new characterizations of $\alpha $-spaces are also obtained.},
author = {Lo Faro, Giovanni, Nordo, Giorgio, Porter, Jack R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\alpha $-space; $\alpha T_i$-space; minimal-$\alpha T_i$ space; $T_2$-closed space; minimal-$T_2$ space; $\psi $-space; -space; -space; -closed space; minimal- space; -space},
language = {eng},
number = {4},
pages = {727-740},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On minimal-$\alpha $-spaces},
url = {http://eudml.org/doc/249175},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Lo Faro, Giovanni
AU - Nordo, Giorgio
AU - Porter, Jack R.
TI - On minimal-$\alpha $-spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 4
SP - 727
EP - 740
AB - An $\alpha $-space is a topological space in which the topology is generated by the family of all $\alpha $-sets (see [N]). In this paper, minimal-$\alpha \mathcal {P}$-spaces (where $\mathcal {P}$ denotes several separation axioms) are investigated. Some new characterizations of $\alpha $-spaces are also obtained.
LA - eng
KW - $\alpha $-space; $\alpha T_i$-space; minimal-$\alpha T_i$ space; $T_2$-closed space; minimal-$T_2$ space; $\psi $-space; -space; -space; -closed space; minimal- space; -space
UR - http://eudml.org/doc/249175
ER -

References

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  1. Dontchev J., Survey on pre-open sets, preprint, 1999. 
  2. Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  3. Larson R., Minimal T 0 -spaces and minimal T D -spaces, Pacific J. Math. 31 (1969), 451-458. (1969) MR0251688
  4. Levine N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. (1963) Zbl0113.16304MR0166752
  5. Lo Faro G., Su alcune proprietà degli insieme α -aperti, Atti Sem. Mat. Fis. Univ. Modena XXIX (1980), 242-252 (in Italian). (1980) 
  6. Njåstad O., On some classes of nearly open sets, Pacific J. Math. 15 3 (1965), 961-970. (1965) MR0195040
  7. Porter J.R., Woods R.G., Extensions and Absolutes of Hausdorff Spaces, Springer, New York, 1988. Zbl0652.54016MR0918341
  8. Tall F.D., The density topology, Pacific J. Math. 62 (1976), 275-284. (1976) Zbl0305.54039MR0419709

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