David Milovich: On cofinal types in compacta: cubes, squares, and forbidden rectangles

Toronto Set Theory Seminar
Friday, October 21 from 1:30 to 3pm
Fields, room 210 or Library room

Speaker: David Milovich (Texas A&M International)

Title: On cofinal types in compacta: cubes, squares, and forbidden rectangles

Abstract:
In every compactum, not every point’s neighborhood filter has cofinal type omega times omega_2. (This is an instance of a more general theorem.) This can be interpreted as yet another partial result pointing toward the conjectures that homogeneous compacta cannot have cellularity greater than c (Van Douwen’s Problem) nor an exponential gap between character and pi-character. There are compacta where every point’s neighborhood filter has cofinal type omega times omega_1, but it is not known if there is a homogeneous compactum with this property.

Continuing the theme of cofinal types of product orders, the Fubini cube and Fubini square of an arbitrary filter F on omega are cofinally equivalent to each other and to the direct product F^omega. (This generalizes to kappa-complete filters on regular kappa.)

Set Theory and C* algebras
Friday, October 21 from 11am to 1pm
Fields Institute, third floor

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