Results 261 to 270 of about 13,911 (297)

Separation of two convex sets in convexity structures

Journal of Geometry, 1994
The well known notion of convex structure is a generalization of the classical notion of convexity in affine spaces: Let \(X\) be a nonempty set and \({\mathcal C}\) a collection of its subsets. The pair \((X, {\mathcal C})\) is a convex structure (called also a convexity structure) provided that \(\emptyset, X \in {\mathcal C}\) and \({\mathcal C ...
VÍCTOR Chepoi
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Convexity conditions and normal structure of Banach spaces

Journal of Mathematical Analysis and Applications, 2008
We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity.
Satit Saejung
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Convexity in topological betweenness structures

Topology and its Applications, 2021
A betweenness structure is a pair \(\langle X,[\cdot,\cdot,\cdot] \rangle\), where \(X\) is a set and \([\cdot,\cdot,\cdot]\subset X^{3}\) is a ternary relation satisfying that \begin{itemize} \item[(B1)] Inclusivity: \((\forall\ xy )\) \(([x,y,y] \wedge [x,x,y])\) \item[(B2)] Symmetry: \((\forall\ xzy )\) \(([x,z,y] \rightarrow [y,z,x])\) \item[(B3 ...
Anderson, Daron, Bankston, Paul, McCluskey, Aisling   +2 more
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Dimension of Binary Convex Structures

Proceedings of the London Mathematical Society, 1984
It is shown that for compact spaces with a normal binary convexity, the dimension functions dim, ind, Ind, and cohomological dimension are all equal. Also, an H-dimensional compact space X with a normal binary convexity embeds in a product of an M-dimensional connected quotient of X with the space of Xcomponents.
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Convex Structures and Effect Algebras

International Journal of Theoretical Physics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Convex Structures and Continuous Selections

Canadian Journal of Mathematics, 1959
This paper continues the study of continuous selections begun in (13; 14; 15) and the expository paper (12). The purpose of these papers, which is described in detail in the introduction to (13), can be summarized here as follows. If X and Y are topological spaces, and ϕ a function (called a carrier) from X to the space 2Y of non-empty subsets of F ...
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The W*-convexity and normal structure in banach spaces

Applied Mathematics Letters, 2004
Let X be a Banach space, S(X) - {x ε X : ‖#x02016; = 1} be the unit sphere of X.The parameter, modulus of W*-convexity, W*(ε) = inf{ : x, y ɛ S(X), ‖x − y‖ ≥ ε, fx ɛ Δx}, where 0 ≤ ε ≤ 2 and Δx ⊆ S(X*) be the set of norm 1 supporting functionals of S(X ...
Gao, J.
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Structure of Efficient Sets for Convex Objectives

Mathematics of Operations Research, 1989
This paper considers multiple objective problems in which each objective is the minimization of a convex function defined over a convex solution space, and for which the number of objectives is greater than the dimension of the solution space. Such problems arise in location analysis, where the solution space of possible facility sites may be ...
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Modulus of convexity in Banach spaces

Applied Mathematics Letters, 2003
Let X be a Banach space, X2 ⊆ X be a two-dimensional subspace of X, and S(X) = {x ϵ X, ‖x‖ = 1} be the unit sphere of X. Let δ(ϵ) = inf{1 − ‖x + y‖2 : ‖x − y‖ ≤ ϵ}, where x, y ϵ S(X2) and 0 ≤ ϵ ≤ 2 is the modulus of convexity of X.
Gao, J
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The convex structure of electrons

International Journal of Quantum Chemistry, 1977
The treatment of the complex structure of electrons includes a mathematically complete solution of the N-representability problem, enumeration of some of the known necessary conditions for N-representability, some numerical calculations, and some possible lines for further research. (JFP)
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