Complexes are spaces with a<i>σ</i>-almost locally finite base

Abstract

In this paper, we introduce the notion of Z)-complexes which are defined by replacing metric spaces with Nagami's D-spaces in the definition of Hyman's M-spaces, and prove a main theorem that every D-complex is a space with a -almost locally finite base (this notion was introduced by Ito and Tamano). This theorem sharpens a theorem of Nagata. Furthermore, we deal with the adjunction spaces of two spaces with a -almost locally finite base.