The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets
Copyright policy )The completeness of a normed space is equivalent to the homogeneity of its space of closed bounded convex sets
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.
Повнота, нормовані простори, топологічна гомогенність, замкнені опуклі множини, Полнота, нормированные пространства, топологическая гомогенность, замкнутые выпуклые множества, completeness, Completenes, QA1-939, topological homogeneity, normed spaces, Completeness, normed spaces, topological homogeneity, closed convex sets, Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness), Mathematics, closed convex sets
Повнота, нормовані простори, топологічна гомогенність, замкнені опуклі множини, Полнота, нормированные пространства, топологическая гомогенность, замкнутые выпуклые множества, completeness, Completenes, QA1-939, topological homogeneity, normed spaces, Completeness, normed spaces, topological homogeneity, closed convex sets, Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness), Mathematics, closed convex sets
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!