C-embedded Σ-spaces

Milton Don Ulmer

Vol. 46 (1973), No. 2, 591–602

DOI: 10.2140/pjm.1973.46.591

Abstract

Let X = ∏ _α∈AX_α be a product space and p ∈ X. For each ordinal γ the Σ-space Σ_γ(p) is given by: Σ_γ(p) = {x ∈ X card ({α ∈ A : x_α≠p_α}) < ℵ_r}. It is shown that under various hypotheses on X, each continuous reaI-valued function on Σ_γ(p) extends continuously over X. A counterexample is constructed to show these hypotheses cannot be weakened in various ways.

Mathematical Subject Classification 2000

Primary: 54C45

Milestones

Received: 14 August 1971

Published: 1 June 1973