A topological space has calibre $ \aleph_1$ if for every uncountable sequence $ \langle U_\alpha\mid\alpha\lt\aleph_1\rangle$ of nonempty open sets $ U_\alpha\subset X$ , there is an uncountable subfamily $ \Lambda\subset\aleph_1$ with $ \bigcap_{\alpha\in\Lambda}U_\alpha\neq\emptyset$ . Is there a calibre $ \aleph_1$ Moore space which is not separable? (Under CH, the answer is no, since every firstRead more
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