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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Condensations of projective sets onto compacta


Author: Henryk Michalewski
Journal: Proc. Amer. Math. Soc. 131 (2003), 3601-3606
MSC (2000): Primary 54C35, 03E15, 28A05, 54H05
Published electronically: April 1, 2003
MathSciNet review: 1991774
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Abstract: For a coanalytic-complete or ${\vtop{\hbox{${\boldsymbol{\Pi}}^{1}_{2}$ } \kern-4pt \hbox{\kern4pt$\widetilde{}$ }\kern-6pt}} $-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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Additional Information

Henryk Michalewski
Affiliation: Institute of Mathematics, Warsaw University, S. Banach 2 st., 02–097 Warsaw, Poland
Email: henrykm@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06882-5
PII: S 0002-9939(03)06882-5
Keywords: Function spaces, topology of pointwise convergence, condensation, coanalytic set, projective set, uniformization
Received by editor(s): December 12, 2001
Received by editor(s) in revised form: May 21, 2002
Published electronically: April 1, 2003
Additional Notes: The author’s research was partially supported by KBN Grant 5PO3A02321
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society