The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets | Zendy

Ivan Hetman | Zendy

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The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets

Author(s) -

Ivan Hetman

Publication year - 2013

Publication title -

carpathian mathematical publications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.63

H-Index - 4

eISSN - 2313-0210

pISSN - 2075-9827

DOI - 10.15330/cmp.5.1.44-46

Subject(s) - mathematics , bounded function , homogeneity (statistics) , regular polygon , completeness (order theory) , normed vector space , space (punctuation) , strictly convex space , pure mathematics , discrete mathematics , subderivative , mathematical analysis , statistics , convex optimization , computer science , geometry , operating system

We prove that an infinite-dimensional normed space $X$ is complete if and only if the space $\mathrm{BConv}_H(X)$ of all non-empty bounded closed convex subsets of $X$ is topologically homogeneous.

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