Boundedness, one-point extensions and B-extensions

Mathematica Slovaca

Federico Panduri¹  Alessandro Caterino¹  M. Vipera¹ 

关键词: boundedness;    one-point extension;    B-extension;   

DOI  :  10.2478/s12175-007-0058-8

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

The general concept of boundedness in a topological space generalizes both metric boundedness and relative compactness. A one-point extension o(ℱ X) of the space X is naturally associated to each boundedness ℱ X and every Hausdorff one-point extensions of a space X can be obtained in this way. Imitating this construction, it is possible to define a much more general class of Hausdorff extensions of a locally bounded space with respect to a given boundedness, the so-called B-extensions. In this paper we study separation properties and metrizability of this kind of extension.

【 授权许可】

Unknown