4,384 research outputs found
Reduced Coproducts of Compact Hausdorff Spaces
By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the reduced coproduct , which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the ultracoproduct can be obtained from the usual topological ultraproduct via a compactification process in the style of Wallman and Frink. We prove theorems dealing with the topological structure of reduced coproducts (especially ultracoproducts) and show in addition how one may use this construction to gain information about the category of compact Hausdorff spaces
Independences and Partial -Transforms in Bi-Free Probability
In this paper, we examine how various notions of independence in
non-commutative probability theory arise in bi-free probability. We exhibit how
Boolean and monotone independence occur from bi-free pairs of faces and
establish a Kac/Loeve Theorem for bi-free independence. In addition, we prove
that bi-freeness is preserved under tensoring with matrices. Finally, via
combinatorial arguments, we construct partial -transforms in two settings
relating the moments and cumulants of a left-right pair of operators
- …