Virtual Special Issue - International Conference on Topology, Messina (ICTM2015)Lower-Vietoris-type topologies on hyperspaces

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 [4] (it was called there Tychonoff-type hypertopology). We study this new hypertopology and, in particular, we generalize many results from [3]. As a corollary, we get that for every continuous map f:X⟶X, where X is a continuum, there exist a subcontinuum K of X such that f(K)=K.