Generic continuity of restricted weak upper semi-continuous set-valued mappings |
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Authors: | J R Giles and W B Moors |
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Institution: | (1) Department of Mathematics, The University of Newcastle, 2308 Newcastle, NSW, Australia;(2) Simon Fraser University, V5A 1S6 Burnaby, BC, Canada |
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Abstract: | Set-valued mappings from a topological space into subsets of a Banach space which satisfy a restricted form of weak upper semi-continuity, have particularly noteworthy properties. We establish a selection theorem for certain set-valued mappings from a (-) unfavourable topological space into subsets of a Banach space and as a consequence derive the property that restricted weak upper semi-continuous set-valued mappings which satisfy a minimality condition, from a (-) unfavourable topological space into subsets of a Banach space are single-valued and norm upper semi-continuous at the points of a residual subset of their domain. |
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Keywords: | Primary: 54C60 54C65 secondary: 90D05 |
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