Projective $π$-character bounds the order of a $π$-base
Year: 2007
Type: preprint
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.
Authors: Juhasz, Istvan, Szentmiklossy, Zoltan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394659188