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Projective $π$-character bounds the order of a $π$-base

Istvan Juhasz·Zoltan Szentmiklossy
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Abstract

All spaces below are Tychonov. We define the projective pi-character p(X) of a space X as the supremum of the values $πχ(Y)$ where Y ranges over all continuous images of X. Our main result says that every space X has a pi-base whose order is at most p(X), that is every point in X is contained in at most p(X)-many members of the pi-base. Since p(X) is at most t(X) for compact X, this provides a significant generalization of a celebrated result of Shapirovskii.

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Istvan Juhasz, Zoltan Szentmiklossy. 2007-03-28. Projective $π$-character bounds the order of a $π$-base. https://arxiv.org/abs/math/0703835

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