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Compactifications and universal spaces in extension theory

Alex Chigogidze
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Abstract

We show that for each countable simplicial complex P the following conditions are equivalent: (1) $P \in AE(X)$ iff $P \in AE(βX)$ for any space X; (2) There exists a P-invertible map of a metrizable compactum X with $P \in AE(X)$ onto the Hilbert cube.

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Alex Chigogidze. 1999-08-15. Compactifications and universal spaces in extension theory. https://arxiv.org/abs/math/9908073

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