Locally precompact groups: Local realcompactness and connectedness - Mathematics > General TopologyReport as inadecuate




Locally precompact groups: Local realcompactness and connectedness - Mathematics > General Topology - Download this document for free, or read online. Document in PDF available to download.

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.



Author: W. W. Comfort, G. Luk√°cs

Source: https://arxiv.org/







Related documents