Locally precompact groups: (Local) realcompactness and connectedness

Details Locally precompact groups: (Local) realcompactness and connectedness Locally precompact groups: (Local) realcompactness and connectedness

2009-02-13

arxiv.org/abs/0902.2258v3

Journal of Lie Theory 20 (2010) 347-374

Mathematics

General Topology

v3 (published version)

Scientific paper

A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties: Dieudonn\'e completeness; local realcompactness; realcompactness; hereditary realcompactness; connectedness; local connectedness; zero-dimensionality. They also prove that an abelian locally precompact group occurs as the quasi-component of a topological group if and only if it is precompactly generated, that is, it is generated algebraically by a precompact subset.

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