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On Some Combinatorial Problems Concerning Geometrical Realizations of Finite and Infinite Families of Sets
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Alexander Kharazishvili
Published/Copyright:
March 11, 2010
Abstract
A version of the precise definition of Euler–Venn diagram for a given family of subsets of a universal set is presented. Certain geometrical properties of such diagrams are discussed and close connections with purely combinatorial problems and with the theory of convex sets are indicated. In particular, some geometrical realizations of uncountable independent families of sets are considered.
Key words and phrases:: Universal set; Euclidean plane; Euler–Venn diagram; Helly's theorem; mutually independent subsets of a universal set
Received: 2007-12-07
Revised: 2008-10-08
Published Online: 2010-03-11
Published in Print: 2008-December
© Heldermann Verlag
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Keywords for this article
Universal set;
Euclidean plane;
Euler–Venn diagram;
Helly's theorem;
mutually independent subsets of a universal set
Articles in the same Issue
- On Iterative Combination of Modified Bernstein-Type Polynomials
- On Dynamical Three-Dimensional Fluid-Solid Interaction Problem
- Existence and Uniqueness of Weak Solution for a Class of Elliptic Reaction-Diffusion Systems
- Existence of Solutions in Weighted Sobolev Spaces for Some Degenerate Quasilinear Elliptic Equations
- Periodic Solutions for Nonlinear Differential Equation with Functional Delay
- Restriction Theorems for Anisotropically Homogeneous Hypersurfaces of
- Dual Variational Method for a Fourth Order Dirichlet Problem
- On Some Combinatorial Problems Concerning Geometrical Realizations of Finite and Infinite Families of Sets
- Beurling–Borg Type Theorem for Two-Dimensional Linear Differential Systems
- The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces
- Sequential Detection of Drift Change for Brownian Motion with Unknown Sign
- Uniqueness for Meromorphic Functions Concerning Differential Polynomials
- Integral Representations and Continuous Projectors in Some Spaces of Analytic and Pluriharmonic Functions
- On One Problem with the Condition at Infinity for Second Order Singular Ordinary Differential Equations
- Rectifiable and Unrectifiable Oscillations for a Generalization of the Riemann–Weber Version of Euler Differential Equation
- Compact Composition Operators on Generalized Hardy Spaces
- CLT for Operator Abel Sums of Random Elements
- On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Whole Boundary of a Multidimensional Domain
- A Note on Conjugacy Classes of Finite Groups
