Generalized ordered spaces with capacities

Harold Bennett and David John Lutzer

Vol. 112 (1984), No. 1, 11–19

DOI: 10.2140/pjm.1984.112.11

Abstract

We show that any GO-space having a capacity in the sense of Ščepin has a G_δ-diagonal and is perfect. In addition, such a space has a σ-discrete dense subset and a dense metrizable subspace, and any GO-space having a capacity and a point-countable base (or having a σ-discrete dense subset and a point-countable base) is metrizable.

Mathematical Subject Classification 2000

Primary: 54F05

Secondary: 54E35

Milestones

Received: 14 May 1982

Published: 1 May 1984