On Ginsburg-Isbell derivatives and ranks of metric spaces

Aarno Hohti

Vol. 111 (1984), No. 1, 39–48

DOI: 10.2140/pjm.1984.111.39

Abstract

The paper deals with the following problem: given a metric space, is there a countable ordinal α such that the α-th successive Ginsburg-Isbell derivative of the metric uniformity contains every open cover of the space? In addition to other results we show that a separable metric space has the above property if and only if it is complete and σ-compact.

Mathematical Subject Classification 2000

Primary: 54E50

Secondary: 54E15, 54E45

Milestones

Received: 20 January 1982

Revised: 5 April 1983

Published: 1 March 1984