Boundedness, one-point extensions and B-extensions

Abstract

Abstract 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.