On Hattori spaces

Commentationes mathematicae Universitatis Carolinae

A. Bouziad ; E. Sukhacheva

关键词: Hattori space;    \\v Cech-complete space;    \\v Cech-analytic space;    neighborhood assignment;    Sorgenfrey line;    scattered set;    weakly separated spaceDOI: DOI 10.14712/1213-7243.2015.199AMS Subject Classification: 54C05 54C35 54C45 54C99 PDF;   

DOI  :  10.14712/1213-7243.2015.199

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 \\v Cech-complete, \\v Cech-complete, quasicomplete, \\v Cech-analytic and weakly separated (in Tkacenko sense). Some of these results solve questions raised by V.A. Chatyrko and Y. Hattori.

【 授权许可】

CC BY