Vietoris-type Topologies on Hyperspaces
Abstract
We introduce a new Vietoris-type hypertopology by means of the upper-Vietoris-type hypertopology defined by G. Dimov and D. Vakarelov [On Scott consequence systems, Fundamenta Informaticae, 33 (1998), 43-70] (it was called there {\em Tychonoff-type hypertopology}) and the lower-Vietoris-type hypertopology introduced by E. Ivanova-Dimova [Lower-Vietoris-type topologies on hyperspaces, Topology Appl. (to appear)]. We study this new Vietoris-type hypertopology and show that it is, in general, different from the Vietoris topology. Also, some of the results of E. Michael [Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182] about hyperspaces with Vietoris topology are extended to analogous results for hyperspaces with Vietoris-type topology. We obtain as well some results about hyperspaces with Vietoris-type topology which concern some problems analogous to those regarded by H.-J. Schmidt [Hyperspaces of quotient and subspaces. I. Hausdorff topological spaces, Math. Nachr. 104 (1981), 271-280].
Cite
@article{arxiv.1701.01181,
title = {Vietoris-type Topologies on Hyperspaces},
author = {Elza Ivanova-Dimova},
journal= {arXiv preprint arXiv:1701.01181},
year = {2017}
}
Comments
15 pages