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Abstract: A theorem of A. Weil asserts that a topological group embeds as a densesubgroup of a locally compact group if and only if it contains a non-emptyprecompact open set; such groups are called locally precompact. Within theclass of locally precompact groups, the authors classify those groups with thefollowing topological properties:Dieudonn\-e completeness; local realcompactness; realcompactness; hereditaryrealcompactness; connectedness; local connectedness; zero-dimensionality. Theyalso prove that an abelian locally precompact group occurs as thequasi-component of a topological group if and only if it is precompactlygenerated, that is, it is generated algebraically by a precompact subset.



Autor: W. W. Comfort, G. Lukács

Fuente: https://arxiv.org/



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