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A: About subspaces of $F$-spaces

JakobianFor definitions of extremally disconnected, $P$-space, basically disconnected (under the name $\sigma$-complete), $F$-spaces, $F'$-spaces, and relations between them, see [3]. A dense subspace of extremally disconnected space is extremally disconnected. This fails horribly for basically disconnec...

Example of a dense subspace of compact basically disconnected space which is not even an $F'$-space

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