2013/11/07 by Istvan Juhasz, Juhasz, Istvan, Lajos Soukup +3
Mathematics · #03E35 #54A25 #54A35 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:03E35 #msc:54A25 #msc:54A35
paper · pdf · doi:10.48550/arxiv.1311.1719
arxiv created 2013/11/07 · arxiv updated 2013/11/08
We improve some results of Pavlov and of Filatova, respectively, concerning a problem of Malychin by showing that every regular space X that satisfies Delta(X)>ext(X) is omega-resolvable. Here Delta(X), the dispersion character of X, is the smallest size of a non-empty open set in X and ext(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are omega-resolvable. We also prove that any regular Lindelöf space X with |X|=Δ(X)=omega1 is even omega1-resolvable. The question if regular Lindelöf spaces of uncountable dispersion character are maximally resolvable remains wide open.