# 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

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