Vol. 46, No. 2, 1973

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C-embedded Σ-spaces

Milton Don Ulmer

Vol. 46 (1973), No. 2, 591–602
Abstract

Let X = αAXα be a product space and p X. For each ordinal γ the Σ-space Σγ(p) is given by: Σγ(p) = {x X card ({α A : xαpα}) < r}. It is shown that under various hypotheses on X, each continuous reaI-valued function on Σγ(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
Authors
Milton Don Ulmer