On Hattori spaces

A. Bouziad; E. Sukhacheva

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 2, page 213-223
  • ISSN: 0010-2628

Abstract

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For a subset A of the real line ℝ , Hattori space H ( A ) is a topological space whose underlying point set is the reals ℝ and whose topology is defined as follows: points from A are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on A which are sufficient and necessary for H ( A ) to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in Tkacenko sense). Some of these results solve questions raised by V.A. Chatyrko and Y. Hattori.

How to cite

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Bouziad, A., and Sukhacheva, E.. "On Hattori spaces." Commentationes Mathematicae Universitatis Carolinae 58.2 (2017): 213-223. <http://eudml.org/doc/288213>.

@article{Bouziad2017,
abstract = {For a subset $A$ of the real line $\mathbb \{R\}$, Hattori space $H(A)$ is a topological space whose underlying point set is the reals $\mathbb \{R\}$ and whose topology is defined as follows: points from $A$ are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on $A$ which are sufficient and necessary for $H(A)$ to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in Tkacenko sense). Some of these results solve questions raised by V.A. Chatyrko and Y. Hattori.},
author = {Bouziad, A., Sukhacheva, E.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hattori space; Čech-complete space; Čech-analytic space; neighborhood assignment; Sorgenfrey line; scattered set; weakly separated space},
language = {eng},
number = {2},
pages = {213-223},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Hattori spaces},
url = {http://eudml.org/doc/288213},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Bouziad, A.
AU - Sukhacheva, E.
TI - On Hattori spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 2
SP - 213
EP - 223
AB - For a subset $A$ of the real line $\mathbb {R}$, Hattori space $H(A)$ is a topological space whose underlying point set is the reals $\mathbb {R}$ and whose topology is defined as follows: points from $A$ are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on $A$ which are sufficient and necessary for $H(A)$ to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in Tkacenko sense). Some of these results solve questions raised by V.A. Chatyrko and Y. Hattori.
LA - eng
KW - Hattori space; Čech-complete space; Čech-analytic space; neighborhood assignment; Sorgenfrey line; scattered set; weakly separated space
UR - http://eudml.org/doc/288213
ER -

References

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