Displaying similar documents to “Varieties of topological groups, Lie groups and SIN-groups”

A decomposition theorem for compact groups with an application to supercompactness

Wiesław Kubiś, Sławomir Turek (2011)

Open Mathematics

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We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.

On universal enveloping algebras in a topological setting

Daniel Beltiţă, Mihai Nicolae (2015)

Studia Mathematica

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We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional...