## Tightness and π-character in centered spaces

### Volume 80 / 1999

Colloquium Mathematicum 80 (1999), 297-307
DOI: 10.4064/cm-80-2-297-307

#### Abstract

We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = sup{κ : $2^κ$ ⊂ X}. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the centered property is not preserved by passage to a zeroset.