A space Cp(X) is dominated by irrationals if and only if it is K-analytic

Vladimir V. Tkachuk

doi:10.1007/s10474-005-0194-y

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Acta Mathematica Hungarica

Volume/Issue:: Volume 107: Issue 4

A space C_p(X) is dominated by irrationals if and only if it is K-analytic

Author: Vladimir V. Tkachuk¹

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¹ Departamento de Matemáticas, Universidad Autónoma Metropolitana Av. San Rafael Atlixco, 186, Col. Vicentina, Iztapalapa, C.P. 09340, México D.F.

DOI:: https://doi.org/10.1007/s10474-005-0194-y

Page Count:: 253–265

Publication Date:: 01 Jun 2005

Online Publication Date:: 31 May 2005

Article Category:: Research Article

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Summary We prove that, for any Tychonoff X, the space C _p(X) is K-analytic if and only if it has a compact cover {K _p: p ? ?^?} such that K _p subset K _q whenever p,q ? ?^? and p = q. Applying this result we show that if C _p(X) is K-analytic then C _p(?X) is K-analytic as well. We also establish that a space C _p(X) is K-analytic and Baire if and only if X is countable and discrete.