The regular open continuous images of complete metric spaces

Howard Henry Wicke

Vol. 23 (1967), No. 3, 621–625

DOI: 10.2140/pjm.1967.23.621

Abstract

This article characterizes the regular T₀ open continuous images of complete metric spaces. These images are shown to be the regular T₀-spaces having monolonically complete bases of countable order. This follows from a theorem of Worrell and Wicke and a theorem below which shows that every regular T₀-space having a monotonically complete base of countable order is an open continuous image of a complete metric space.

Mathematical Subject Classification

Primary: 54.35

Milestones

Received: 23 August 1966

Published: 1 December 1967