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arXiv · 1601.08168

Lower-Vietoris-type Topologies on Hyperspaces

Elza Ivanova-Dimova
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Abstract

We introduce a new lower-Vietoris-type hypertopology in a way similar to that with which a new upper-Vietoris-type hypertopology was introduced in G. Dimov and D. Vakarelov, "On Scott consequence systems", Fundamenta Informaticae, 33 (1998), 43-70. (it was called there {\em Tychonoff-type hypertopology}). We study this new hypertopology and, in particular, we generalize many results from E. Cuchillo-Ibanez, M. A. Moron and F. R. Ruiz del Portal, "Lower semifinite topology in hyperspaces", Topology Proceedings, 17 (1992), 29-39. As a corollary, we get that for every continuous map $f:X\longrightarrow X$, where $X$ is a continuum, there exist a subcontinuum $K$ of $X$ such that $f(K)=K.$

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Elza Ivanova-Dimova. 2016-01-29. Lower-Vietoris-type Topologies on Hyperspaces. https://arxiv.org/abs/1601.08168

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