Complexes are spaces with a σ-almost locally finite base

Takuo Miwa

Vol. 113 (1984), No. 2, 407–416

DOI: 10.2140/pjm.1984.113.407

Abstract

In this paper, we introduce the notion of D-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 σ-almost locally finite base (this notion was introduced by Itō and Tamano). This theorem sharpens a theorem of Nagata. Furthermore, we deal with the adjunction spaces of two spaces with a σ-almost locally finite base.

Mathematical Subject Classification 2000

Primary: 54E20

Milestones

Received: 14 December 1982

Published: 1 August 1984