Cauchy sequences in Moore spaces

Kenneth Edward Whipple

Vol. 18 (1966), No. 1, 191–199

DOI: 10.2140/pjm.1966.18.191

Abstract

In this paper the concept of a Cauchy sequence is extended to Moore spaces. This concept is then used to characterize those Moore spaces which are completable (i.e., topologically equivalent to a subspace of a complete Moore space). The definition for Cauchy sequence given here is shown to be a generalization of the usual definition for Cauchy sequence in a metric space. Also considered are certain questions concerning completability of a Moore space having a dense complelable subspace.

Mathematical Subject Classification

Primary: 54.38

Milestones

Received: 20 February 1965

Published: 1 July 1966