On Generalization of k-space
Dewi Kartika Sari, Zhao Dongsheng

FMIPA UGM,
MME-NIE NTY

Abstract

In this paper, we study a generalization of -k--space, a topological space that is closely related to locally compact spaces. A topological space -(X, \tau )- is called -S--defined if -A \substeq X- is open, whenever -A \cap K- is open in -K- for any -K &#8712- S(X)-, where -S(X)- is a family of subsets of -X-. By considering different families S(X), we obtain different types of spaces. In particular, we show that the Scott spaces of posets are -S--defined.

Keywords: -k--space, locally compact, Scott space

Topic: Others