Some Properties of Rectifiable Spaces

Abstract

In this paper, we give some properties of rectifiable spaces and their relationship with P-space, metrizable space. These results are used to generalize some results in [2], [9] and [12]. Moreover, we give the conditions for a rectifiable space to be second-countable.

The Vietoris hyperspace $\mathcal F(X)$ and certain generalized metric properties

“…Recently, the generalized metric properties on hyperspaces with the Vietoris topology have been studied by many authors ( [8], [10], [16], [17], [20], [21], [22]). They considered several generalized metric properties and studied the relation between a space X satisfying such a property and its hyperspaces with the Vietoris topology, such as the n-fold symmetric product F n (X), the hyperspace F(X) of finite subsets of X satisfying the same property.…”