2016/01/29 by Ivanova-Dimova, Elza
#54B20 #54C05 #54F15 #54H25 #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1601.08168
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.