Metrization of spaces with countable large basis dimension

Gary Fred Gruenhage and Phillip Lee Zenor

Vol. 59 (1975), No. 2, 455–460

DOI: 10.2140/pjm.1975.59.455

Abstract

With the following results, we generalize known metrization theorems for spaces with large basis dimension 0 i.e., non-archimedian spaces) to the higher dimensions: Theorem. If X is a normal Σ-space with countable large basis dimension, then X is metrizable. Theorem. If X is a normal wΔ-space with countable large basis dimension, then X is metrizable.

Mathematical Subject Classification 2000

Primary: 54E35

Secondary: 54F45

Milestones

Received: 22 January 1975

Revised: 3 June 1975

Published: 1 August 1975