Open--constructible functions

Alexey Ostrovsky

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arXiv · 1302.1979

Open--constructible functions

Alexey Ostrovsky

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Abstract

We prove that if a continuous function $f : X \to f(X)$ takes open sets into elements of the Boolean algebra generated by open and closed subsets in $f(X)$, then there exist $X_n \subset X,$ $(n \in \omega)$ such that $f$ is open on every $X_n$ and $f(X_n)$ cover $ f(X).$

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Alexey Ostrovsky. 2013-02-08. Open--constructible functions. https://arxiv.org/abs/1302.1979

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