A hereditary property in locally convex spaces
Manuel Valdivia (1971)
Annales de l'institut Fourier
Similarity:
If is an infrabarrelled space, it is proved that any subspace , of finite codimension, is infrabarrelled.
Manuel Valdivia (1971)
Annales de l'institut Fourier
Similarity:
If is an infrabarrelled space, it is proved that any subspace , of finite codimension, is infrabarrelled.
I. Monterde, Vicente Montesinos (2009)
Czechoslovak Mathematical Journal
Similarity:
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 of a locally convex space is the -closure of the union of countably many -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
B. Mirković (1970)
Matematički Vesnik
Similarity:
Taras Banakh, Ivan Hetman (2012)
Studia Mathematica
Similarity:
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 of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a...
Fethi Kadhi (2002)
RAIRO - Operations Research - Recherche Opérationnelle
Similarity:
We investigate the minima of functionals of the form where is strictly convex. The admissible functions are not necessarily convex and satisfy on , , , is a fixed function on . We show that the minimum is attained by , the convex envelope of .
Zbigniew Lipecki (2011)
Colloquium Mathematicae
Similarity:
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).
Janusz Januszewski, Stanislaw Szufla (1992)
Publications de l'Institut Mathématique
Similarity:
Surjit Singh Khurana (2001)
Czechoslovak Mathematical Journal
Similarity:
Let be a completely regular Hausdorff space, the space of all scalar-valued bounded continuous functions on 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 -convex.
M. Obradović, S. Owa (1986)
Matematički Vesnik
Similarity: