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Baire sets and the Boolean reflection of sigma-frames
 
 
Description:  For any topological space X, the σ-field BX of its Baire sets is the Boolean sub-σ-algebra of the power set of X generated by the σ-frame Coz X of the cozero sets of X. Apart from this, one obviously has the abstractly defined Boolean σ-frame reflection BCoz X and the homomorphism ΦX:BCoz X --> BX determined by the identical embedding Coz X --> BX. Consequently, this raises the question about the nature of ΦX, in particular the problem for which X it is an isomorphism. This talk will present a number of results concerning this, among others that, for any countable Tychonoff space X, ΦX is an isomorphism iff X is scattered (= every non-void subspace of X has an isolated point) and a new proof of the fact, due to Madden-Vermeer, that ΦX is an isomorphism for any compact Tychonoff X.
Date:  2011-06-30
Start Time:   14:30
Speaker:  Bernhard Banaschewski (McMaster University, Canada)
Institution:  McMaster University
Research Groups: -Algebra, Logic and Topology
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