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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
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Direct proof of "K is projective iff C(K) has the Hahn-Banach property" ?
Maybe I made a stupid mistake, but I think something along the following lines should work:
Let $1_K$ be the standard order unit of $C(K)$. There is a canonical identification of $K$ with the subset …