Countable-dimensional universal sets

Pol, Roman

doi:10.1090/S0002-9947-1986-0849478-7

Countable-dimensional universal sets
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Trans. Amer. Math. Soc. 297 (1986), 255-268 Request permission

Abstract:

The main results of this paper are a construction of a countable union of zero dimensional sets in the Hilbert cube whose complement does not contain any subset of finite dimension $n \geqslant 1$ (Theorem 2.1, Corollary 2.3) and a construction of universal sets for the transfinite extension of the Menger-Urysohn inductive dimension (Theorem 2.2, Corollary 2.4).

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