


Baire sets and the Boolean reflection of sigmaframes



Description: 
For any topological space X, the σfield BX of its Baire sets is the Boolean subσalgebra of the power set of X generated by the σframe Coz X of the cozero sets of X. Apart from this, one obviously has the abstractly defined Boolean σframe reflection BCoz X and the homomorphism Φ_{X}:BCoz X > BX determined by the identical embedding Coz X > BX. Consequently, this raises the question about the nature of Φ_{X}, 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, Φ_{X} is an isomorphism iff X is scattered (= every nonvoid subspace of X has an isolated point) and a new proof of the fact, due to MaddenVermeer, that Φ_{X} is an isomorphism for any compact Tychonoff X.

Date: 
20110630

Start Time: 
14:30 
Speaker: 
Bernhard Banaschewski (McMaster University, Canada)

Institution: 
McMaster University

Research Groups: 
Algebra, Logic and Topology

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