Type: Inproceedings

Extreme selections for hyperspaces of topological spaces

S. García-Ferreira; V. Gutev; T. Nogura; M. Sanchis; A. Tomita;

Book Title: Proceedings of the International Conference on Topology and its Applications (Yokohama, 1999)

Abstract:

We study properties of Hausdorff spaces X which depend on the variety of continuous selections for their Vietoris byperspaces F(X) of closed non-empty subsets. Involving extreme selections for F(X), we characterize several classes of connected-like spaces. In the same way, we also characterize several classes of disconnected-like spaces, for instance all countable scattered metrizable spaces. Further, involving another type of selections for F(X), we study local properties of X related to orderability. In particular, we characterize some classes of orderable spaces with only one non-isolated point