Hausdorff CCC spaces with countable centered local π-bases at each point satisfy |X| ≤ 𝔠, strictly improving Hajnal-Juhász 1967 and Pospíšil 1937.
Pospi ˇsil,Sur la puissance d’un espace contenant une partie dense de puissance donn ´ee, ˇCasopis Pestov´ani Matematiky a Fysiky67(1937), 89–96
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On centered local $\pi$-bases
Hausdorff CCC spaces with countable centered local π-bases at each point satisfy |X| ≤ 𝔠, strictly improving Hajnal-Juhász 1967 and Pospíšil 1937.