Hausdorff CCC spaces with countable centered local π-bases at each point satisfy |X| ≤ 𝔠, strictly improving Hajnal-Juhász 1967 and Pospíšil 1937.
Carlson,A survey of bounds on the cardinality of a Hausdorff space, Top
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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.