Murray Bell - Cardinal functions of centered spaces

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Murray Bell - Cardinal functions of centered spaces

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

Cardinal functions of centered spaces

For a collection of sets S, give $\textrm{cen}(S) = \{T \subset S : T$ is centered $\}$ the compact Hausdorff topology that it inherits as a subspace of 2S. The spaces cen(S) are exactly the Adequate Compact spaces of Talagrand. They have served topologists well as a rich source of examples. This talk is concerned with spaces which are by definition those Hausdorff spaces that are continuous images of some cen(S). This is a good generalization of the dyadic spaces. Our focus will be on the relationships between the 9 popular cardinal functions of w, $\pi$ , t, $\chi$ , d, c, $\pi\chi$ , $d\chi$ and $d\pi\chi$ for this class of spaces.

Next: Maxim R. Burke - Up: 3) Set Theoretic Topology / Previous: 3) Set Theoretic Topology /