Dense families of selections and finite-dimensional spaces

V. Gutev; V. Valov

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arXiv · math/0111254

Dense families of selections and finite-dimensional spaces

V. Gutev·V. Valov

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Abstract

A characterization of $n$-dimensional spaces via continuous selections avoiding $Z_n$-sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem and to obtain a new alternative proof of the Hurewicz formula.

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V. Gutev, V. Valov. 2001-11-26. Dense families of selections and finite-dimensional spaces. https://arxiv.org/abs/math/0111254

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