# Projective -character bounds the order of a -base

István Juhász, and Zoltán Szentmiklóssy

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

Key words and phrases: Projective pi-character, order of a pi-base, irreducible map

2000 Mathematics Subject Classification: 54A25, 54C10, 54D70