We consider a number of very strong separation properties for connected spaces. A space X is finitely separated provided each separator between two points of X contains a finite separator between those two points. If (X, T) is a connected, Hausdorff, finitely separated space then there is a weaker topology W for X such that (X,W) embeds in a finitely separated continuum. We give several characterizations of finitely separated continua and show that under mild conditions finitely separated spaces are ANRs.
© 2001-2024 Fundación Dialnet · Todos los derechos reservados