A note on Stone’s, Baire’s, Ky Fan’s and Dugundji’s theorem in tvs-cone metric spaces
Copyright policy )A note on Stone’s, Baire’s, Ky Fan’s and Dugundji’s theorem in tvs-cone metric spaces
The article relates to generalizations of some aspects of Dugundji's extension theorem and related issues to the so-called cone metric spaces. The cone is assumed solid which opens way to the standard scalarization. The author views as the distinction of her analysis the fact that the cones in topological vector spaces she considers may fail to be normal. Reviewer's remark. Analogous general results, free of the interior point assumption, are straightforward within Boolean valued analysis; see, for instance, [\textit{A. G. Kusraev} and \textit{S. S. Kutateladze}, ``Introduction to Boolean-valued analysis'' (in Russian) (Moskva: Nauka) (2005; Zbl 1087.03032)].
tvs-cone metric space, Dugundji's extension theorem, Fixed-point and coincidence theorems (topological aspects), Paracompact space, Applied Mathematics, Dugundji’s extension theorem, tvs-cone metric, scalarisation, Special maps on metric spaces
tvs-cone metric space, Dugundji's extension theorem, Fixed-point and coincidence theorems (topological aspects), Paracompact space, Applied Mathematics, Dugundji’s extension theorem, tvs-cone metric, scalarisation, Special maps on metric spaces
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