Quasimetrizable spaces

Jacob Kofner

Vol. 88 (1980), No. 1, 81–89

DOI: 10.2140/pjm.1980.88.81

Abstract

A construction is given which yields to any quasi-metrizable not non-archimedeanly quasi-metrizable space another quasi-metrizable space which is not σ-orthocompact. It is shown that (σ-)orthocompactness does not imply non-archimedean quasi-metrizability and is neither summable nor multiplicative nor (CH) hereditary in completely regular quasi-metric spaces.

It is proved that quasi-metric spaces are preserved under perfect mappings.

Mathematical Subject Classification 2000

Primary: 54E35

Secondary: 54E15

Milestones

Received: 3 March 1978

Revised: 31 May 1978

Published: 1 May 1980