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

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

2007-03-28

arxiv.org/abs/math/0703835v1

Mathematics

General Topology

7 pages

Scientific paper

All spaces below are Tychonov. We define the projective pi-character p(X) of a space X as the supremum of the values $\pi\chi(Y)$ 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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