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Proceedings of the American Mathematical Society

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

 

 

Totally analytic spaces under $ V=L$


Authors: Zoltán Balogh and Heikki Junnila
Journal: Proc. Amer. Math. Soc. 87 (1983), 519-527
MSC: Primary 54H05; Secondary 03E35
DOI: https://doi.org/10.1090/S0002-9939-1983-0684650-3
MathSciNet review: 684650
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Abstract: The following results obtain under the axiom of constructibility $ (V = L)$:

Assume that every subset of a topological space $ X$ is analytic. Then $ X$ is $ \sigma $-left-separatcd. Moreover, if the character of $ X$ is $ \leqslant {\omega _1}$, then $ X$ is $ \sigma $-discrete.

Assume that $ X$ is a perfectly normal space of character $ \leqslant {\omega _1}$ such that every subset of $ X$ belongs to the $ \sigma $-algebra generated by the analytic subsets of $ X$. Then $ X$ is $ \sigma $-discrete.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0684650-3
Keywords: $ V = L$, analytic set, $ \sigma $-discrete, left-separated, character
Article copyright: © Copyright 1983 American Mathematical Society