Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers
From MaRDI portal
Publication:2551969
DOI10.2140/pjm.1971.38.471zbMath0235.52001OpenAlexW1994744765WikidataQ56503425 ScholiaQ56503425MaRDI QIDQ2551969
Eugene W. Womble, David C. Kay
Publication date: 1971
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2140/pjm.1971.38.471
Related Items (56)
Separation of two convex sets in convexity structures ⋮ Generalised Helly and Radon numbers ⋮ Flat transversals to flats and convex sets of a fixed dimension ⋮ Colorful Carathéodory, Helly and sierksma numbers of convexity spaces ⋮ The starshapedness number and a Krasnosel'skij-type theorem in a convexity space ⋮ Kakutani property of the polytopes implies Kakutani property of the whole space ⋮ Subdifferentiation of monotone functions from semilattices to distributive lattices ⋮ Fixed point theorems for the class S-KKM mappings in abstract convex spaces ⋮ Subcategories of the category of \(L\)-convex spaces ⋮ On the investigations of Ivan Prodanov in the theory of abstract spectra ⋮ Visibility in semi-convex spaces ⋮ Convex sets in graphs. II: Minimal path convexity ⋮ LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies ⋮ Convexity in ordered matroids and the generalized external order ⋮ A more refined convexity idea for Nash equilibria ⋮ Ball and spindle convexity with respect to a convex body ⋮ Efficient realizations of closure systems ⋮ First-order logic axiomatization of metric graph theory ⋮ Unnamed Item ⋮ A Tverberg-type generalization of the Helly number of a convexity space ⋮ Antimatroids, Betweenness, Convexity ⋮ Helly numbers of algebraic subsets of \(\mathbb{R}^{d}\) and an extension of Doignon's theorem ⋮ Helly’s theorem: New variations and applications ⋮ Generalized Radon partitions in convexity spaces ⋮ Euclidean convexity cannot be compactified ⋮ Generalized monotonically \(T_2\) spaces ⋮ Restricted-oriented convex sets ⋮ On weak \(\epsilon\)-nets and the Radon number ⋮ Turán theorems and convexity invariants for directed graphs ⋮ A canonical decomposition theory for metrics on a finite set ⋮ Graphs with intrinsic s3 convexities ⋮ Pseudo-median graphs are join spaces ⋮ Joint pseudo-utility representations ⋮ Eine kategorische Charakterisierung von Familien konvexer Mengen ⋮ Two-dimensional convexities are join-hull commutative ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Axiomatic theory of convexity ⋮ KKM lemmas and minimax inequality theorems in abstract convexity spaces ⋮ Polynomial Time Algorithms for Computing a Minimum Hull Set in Distance-Hereditary and Chordal Graphs ⋮ Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of $S$-optimization ⋮ Unnamed Item ⋮ Parametrization of knowledge structures ⋮ Spot functions and peripherals: Krein-Milman type theorems in an abstract setting ⋮ Finite dimensional convex structures. II: The invariants ⋮ Approximate fixed point theorems for the class of almost S-KKM\(_{\mathcal C}\) mappings in abstract convex uniform spaces ⋮ A decompositin theorem for convexity spaces ⋮ Unnamed Item ⋮ The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg ⋮ Finite dimensional convex structures. I: General results ⋮ Intersecting sets in midsets spaces. II ⋮ Unnamed Item ⋮ Unified treatment of the problem of existence of maximal elements in binary relations: A characterization ⋮ Combinatorial geometry ⋮ Matching binary convexities ⋮ A topological approach to structure theory, I
This page was built for publication: Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers
