Displaying similar documents to “ p -Spaces and injective locally convex spaces”

Convex-compact sets and Banach discs

I. Monterde, Vicente Montesinos (2009)

Czechoslovak Mathematical Journal

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Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual E ' of a locally convex space E is the σ ( E ' , E ) -closure of the union of countably many σ ( E ' , E ) -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.

A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

Taras Banakh, Ivan Hetman (2012)

Studia Mathematica

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A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space C o n v ( X ) of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a...

Generalized characterization of the convex envelope of a function

Fethi Kadhi (2002)

RAIRO - Operations Research - Recherche Opérationnelle

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We investigate the minima of functionals of the form [ a , b ] g ( u ˙ ( s ) ) d s where g is strictly convex. The admissible functions u : [ a , b ] are not necessarily convex and satisfy u f on [ a , b ] , u ( a ) = f ( a ) , u ( b ) = f ( b ) , f is a fixed function on [ a , b ] . We show that the minimum is attained by f ¯ , the convex envelope of f .

Cardinality of some convex sets and of their sets of extreme points

Zbigniew Lipecki (2011)

Colloquium Mathematicae

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We show that the cardinality of a compact convex set W in a topological linear space X satisfies the condition that = . We also establish some relations between the cardinality of W and that of extrW provided X is locally convex. Moreover, we deal with the cardinality of the convex set E(μ) of all quasi-measure extensions of a quasi-measure μ, defined on an algebra of sets, to a larger algebra of sets, and relate it to the cardinality of extrE(μ).

Strict topologies as topological algebras

Surjit Singh Khurana (2001)

Czechoslovak Mathematical Journal

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Let X be a completely regular Hausdorff space, C b ( X ) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m -convex.