Quotients with Respect to Locally Compact Subgroups

• Autores: Alexander V. Arhangel'skii
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 1, 2005, págs. 215-226
• Idioma: inglés
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• Resumen

  • We establish that, for any locally compact subgroup H of a topological group G, the natural quotient mapping of G onto the quotient space G/H is locally perfect, that is, the restriction of it to the closure of some open set is an open mapping with compact fibers. We derive from this that many important topological invariants are transfered from the space G/H to G when H is locally compact.