اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSelection properties of the split interval and the Continuum Hypothesis
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Taras Banakh
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We prove that every usco multimap $Phi:Xto Y$ from a metrizable separable space $X$ to a GO-space $Y$ has an $F_sigma$-measurable selection. On the other hand, for the split interval $ddot{mathbb I}$ and the projection $P:ddot{mathbb I}^2to{mathbb I}^2$ of its square onto the unit square ${mathbb I}^2$, the usco multimap $P^{-1}:{mathbb I}^2multimapddot{mathbb I}^2$ has a Borel ($F_sigma$-measurable) selection if and only if the Continuum Hypothesis holds. This CH-example shows that know results on Borel selections of usco maps into fragmentable compact spaces cannot be extended to a wider class of compact spaces.
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