Displaying similar documents to “On Bárány's theorems of Carathéodory and Helly type”

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

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 C o n v ( X ) of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a...

Pairs of sets with convex union.

Ryszard Urbanski (1997)

Collectanea Mathematica

Similarity:

In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.

Convex-compact sets and Banach discs

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 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.

The cancellation law for inf-convolution of convex functions

Dariusz Zagrodny (1994)

Studia Mathematica

Similarity:

Conditions under which the inf-convolution of f and g f □ g ( x ) : = i n f y + z = x ( f ( y ) + g ( z ) ) has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions f : X → ℝ ∪ + ∞ on a reflexive Banach space such that l i m ∥ x ∥ → ∞ f ( x ) / ∥ x ∥ = ∞ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.