The Dugundji extension theorem and extension degree
Katsuya Eda (1995)
Colloquium Mathematicae
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Katsuya Eda (1995)
Colloquium Mathematicae
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Karol Pąk (2014)
Formalized Mathematics
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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...
Pradipta Bandyopadhyaya (1992)
Colloquium Mathematicae
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Nhu Nguyen, Katsuro Sakai (1996)
Colloquium Mathematicae
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Boonpok, Chawalit (2010)
Acta Universitatis Apulensis. Mathematics - Informatics
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Wee-Kee Tang (1999)
Commentationes Mathematicae Universitatis Carolinae
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A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.