On k-spaces, k_R-spaces and k(X)

Ernest A. Michael

Vol. 47 (1973), No. 2, 487–498

DOI: 10.2140/pjm.1973.47.487

Abstract

Two examples of k_R-spaces which are not k-spaces are constructed; one of them is a σ-compact cosmic space, and the other is an ℵ₀-space. On the positive side, a theorem is proved which implies that every σ-compact ℵ₀-space which is a k_R-space must be a k-space.

Mathematical Subject Classification 2000

Primary: 54D50

Milestones

Received: 8 March 1972

Published: 1 August 1973