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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On properties of Rosenthal compacta


Author: Witold Marciszewski
Journal: Proc. Amer. Math. Soc. 115 (1992), 797-805
MSC: Primary 54C35; Secondary 54A25, 54D20
DOI: https://doi.org/10.1090/S0002-9939-1992-1096213-4
MathSciNet review: 1096213
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Abstract: A compact space $ K$ is a Rosenthal compactum if $ K$ can be embedded in the space $ {B_1}(P)$ of the first Baire class functions on $ P$, the irrationals, endowed with the pointwise topology. We show that if $ L$ is compact, $ {C_p}(L)$ (the space of continuous real-valued functions on $ L$ with the pointwise topology) is a continuous image of $ {C_p}(K)$ and $ K$ is a Rosenthal compactum, then $ L$ is also. We prove that in some subclass of Rosenthal compacta (compacta consisting of the first Baire class functions with countable supports) the countable chain condition implies separability. We also show that compacta from this class possess a certain covering property hereditarily.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1096213-4
Article copyright: © Copyright 1992 American Mathematical Society