Condensations of projective sets onto compacta

Michalewski, Henryk

doi:10.1090/S0002-9939-03-06882-5

Condensations of projective sets onto compacta
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by Henryk Michalewski

Proc. Amer. Math. Soc. 131 (2003), 3601-3606

DOI: https://doi.org/10.1090/S0002-9939-03-06882-5

Published electronically: April 1, 2003

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Abstract:

For a coanalytic–complete or $\undertilde {\Pi }^1_2$–complete subspace $X$ of a Polish space we prove that there exists a continuous bijection of $X$ onto the Hilbert cube $[0,1]^{\mathbb {N}}$. This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen. Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

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