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On enveloping semigroups of nilpotent group actions generated by unipotent affine transformations of the torus

Rafał Pikuła (2010)

Studia Mathematica

Let G be a group generated by a set of affine unipotent transformations T: X → X of the form T(x) = A x + α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. We show that the enveloping semigroup E(X,G) of the dynamical system (X,G) is a nilpotent group and find upper and lower bounds on its nilpotency class. Also, we obtain a description of E(X,G) as a quotient space.

On extended frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.

On extension of functors

L. Karchevska, Taras Radul (2012)

Commentationes Mathematicae Universitatis Carolinae

A. Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the definition of normal functor. We investigate as well some topological properties of such extension.

On extension of the group operation over the Čech-Stone compactification

Jan Jełowicki (1993)

Colloquium Mathematicae

The convolution of ultrafilters of closed subsets of a normal topological group is considered as a substitute of the extension onto ( β ) 2 of the group operation. We find a subclass of ultrafilters for which this extension is well-defined and give some examples of pathologies. Next, for a given locally compact group and its dense subgroup , we construct subsets of β algebraically isomorphic to . Finally, we check whether the natural mapping from β onto β is a homomorphism with respect to the extension...

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