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Compactness and countable compactness in weak topologies

W. Kirk (1995)

Studia Mathematica

A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact....

Convex ( L , M ) -fuzzy remote neighborhood operators

Hu Zhao, Li-Yan Jia, Gui-Xiu Chen (2024)

Kybernetika

In this paper, two kinds of remote neighborhood operators in ( L , M ) -fuzzy convex spaces are proposed, which are called convex ( L , M ) -fuzzy remote neighborhood operators. It is proved that these two kinds of convex ( L , M ) -fuzzy remote neighborhood operators can be used to characterize ( L , M ) -fuzzy convex structures. In addition, the lattice structures of two kinds of convex ( L , M ) -fuzzy remote neighborhood operators are also given.

Convexity theories 0 fin. Foundations.

Heinrich Kleisli, Helmut Röhrl (1996)

Publicacions Matemàtiques

In this paper we study big convexity theories, that is convexity theories that are not necessarily bounded. As in the bounded case (see [4]) such a convexity theory Γ gives rise to the category ΓC of (left) Γ-convex modules. This is an equationally presentable category, and we prove that it is indeed an algebraic category over Set. We also introduce the category ΓAlg of Γ-convex algebras and show that the category Frm of frames is isomorphic to the category of associative, commutative, idempotent...

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