κ-Galilean and κ-Carrollian noncommutative spaces of worldlines

SMALL u κ AND LARGE 2 κ FOR SUPERCOMPACT κ

Garti and Shelah [2] state that one can force uκ to be κ+ for supercompact κ with 2κ arbitrarily large, using the technique of Džamonja and Shelah [1]. Here we spell out how this can be done. §

Compactification of κ-Frames

Hahn - Banach theorems for κ - normed spaces

For a new class of topological vector spaces, namely κ-normed spaces, an associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a κ-norm, that is a distance function between a point and a G δ-subset. For it, analogs of the Hahn-Banach theorem are proved.

Noncommutative Differential Calculus on the Κ-minkowski Space

Following the construction of the κ-Minkowski space from the bicrossproduct structure of the κ-Poincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential calculi, which are Lorentz covariant. We show, however, that there exist a fivedimensional differ...

THE CONSISTENCY OF b = κ AND s = κ +

Using finite support iteration of c.c.c. partial orders we provide a model of b = κ < s = κ for κ an arbitrary regular, uncountable cardinal.