About extension of upper semicontinuous multi-valued maps and applications

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dc.creatorAskoura, Youcef
dc.date2008-10-17
dc.date.accessioned2026-07-07T10:10:58Z
dc.date.available2026-07-07T10:10:58Z
dc.descriptionWe formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal subset) of a completely normal (resp. of a normal) space $X$ into the unit interval $[0,1]$ can be extended to the whole space $X$. The extension is upper semicontinuous with nonempty closed convex values. We apply this result for the extension of real semicontinuous functions, the characterization of completely normal spaces, the existence of Gale-Mas-Colell and Shafer-Sonnenschein type fixed point theorems and the existence of equilibrium for qualitative games.
dc.identifierhttps://arxiv.org/abs/0810.3127
dc.identifierhttp://arxiv.org/abs/0810.3127
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171749
dc.subjectGeneral Topology
dc.subject54C60, 54C20
dc.titleAbout extension of upper semicontinuous multi-valued maps and applications
dc.typetext

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