Totally analytic spaces under 𝑉=𝐿

Balogh, Zoltán; Junnila, Heikki

doi:10.1090/S0002-9939-1983-0684650-3

Totally analytic spaces under $V=L$
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by Zoltán Balogh and Heikki Junnila PDF

Proc. Amer. Math. Soc. 87 (1983), 519-527 Request permission

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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