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On Dow's reflection theorem for metrizable spaces
by
Jerry E. Vaughan
University of North Carolina at Greensboro
We consider the reflection theorem of Alan Dow which states: If X is a space in which every subspace of cardinality no more that \aleph1 is metrizable, and X is countably compact, then X is metrizable. We extend this theorem by weakening ``countably compact'' to ``X has a dense set, conditionally compact in X.'' Known examples show that this compactness-like condition on X cannot be weakened to pseudocompactness or feeble compactness.
Date received: February 27, 1997
Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caam-25.