On a theorem by Hoffman and Ramsay

Stelios A. Negrepontis

Vol. 20 (1967), No. 2, 281–282

DOI: 10.2140/pjm.1967.20.281

Abstract

Hoffman and Ramsay recently constructed, using the continuum hypothesis, a proper subalgebra of the algebra C(βN) of all complex-valued continuous functions on βN which is uniformly closed and separates points of βN. (This example settles in the negative a conjecture by Badé and Curtis). The purpose of this note is to indicate that this result does not need the continuum hypothesis.

Mathematical Subject Classification

Primary: 46.65

Milestones

Received: 5 April 1966

Published: 1 February 1967