Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 11.3.2008 |
| Speaker: | Jan Starý, |
| Title: | Witnesses of Non-homogeneity |
| Abstract: | A topological space is homogeneous if every two points can be swapped by an auto-homeomorphism. Among the spaces which are {\bf not} homogeneous, the Boolean spaces, ie totally (extremally) disconnected compacts play a prominent role; these are categorical duals of (complete) Boolean algebras. While extremally disconnected compacts (EDCs) are known to be non-homo\-geneous, standard ZFC proofs don't necessarily give a topological insight into why; the basic proof is a cardinality argument: there are not enough homeomorphisms. A natural question then is to find "witnesses of nonhomogeneity" - pairs of peculiar points that cannot be swapped. Via Stone duality, this is also a search for interesting ultrafilters. |
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