Tightness and π-character in centered spaces

Murray Bell

ArticleOriginal scientific text

Title

Tightness and π-character in centered spaces

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Affiliations

Department of Mathematics University of Manitoba Winnipeg, Manitoba Canada R3T 2N2

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.

Keywords

ENG

centered, tightness, compact, π-character

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Title

Tightness and π-character in centered spaces

Affiliations

Abstract

Keywords

Bibliography