We prove that every complete metric space X that is thin (i.e., every closed subspace has connected uniform quasi components) has the compact separation property (for any two disjoint closed connected subspaces A and B of X there is a compact set K disjoint from A and B such that every neighbourhood of K disjoint from A and B separates A and B). The real line and all compact spaces are obviously thin. We show that a space is thin if and only if it does not contain a certain forbidden configuration. Finally we prove that every metric UA-space (see [Rend. Instit. Mat. Univ. Trieste 25 (1993) 23–56]) is thin. The UA-spaces form a class properly including the Atsuji spaces.
|Autori:||BERARDUCCI A; DIKRANJAN D; PELANT J|
|Titolo:||Uniform quasi components, thin spaces and compact separation|
|Anno del prodotto:||2002|
|Digital Object Identifier (DOI):||10.1016/S0166-8641(01)00132-8|
|Appare nelle tipologie:||1.1 Articolo in rivista|