On combinatorial and set-theoretical aspects of some finite and infinite point sets
-
Tengiz Tetunashvili
Abstract
In this paper, theorems are stated regarding geometrical realizations of finite families of sets, for a given countable family of sets the existence of families of point sets combinatorially strictly ω-isomorphic to this given family of sets, independent families of triangles in the Euclidean plane, also, the existence and extensions of ρ-at-sets, ρ-rt-sets, ρ-ot-sets and ot-sets. These theorems are a continuation of the corresponding results of [6, 7, 8, 5, 3, 4].
Dedicated to Professor Alexander Kharazishvili on the occasion of his 70th birthday
References
[1] M. Aigner and G. M. Ziegler, Proofs from The Book, 3rd ed., Springer, Berlin, 2004. 10.1007/978-3-662-05412-3Suche in Google Scholar
[2] P. Erdös and Z. Füredi, The greatest angle among n points in the d-dimensional Euclidean space, Combinatorial Mathematics (Marseille-Luminy 1981), North-Holland Math. Stud. 75, North-Holland, Amsterdam (1983), 275–283. 10.1016/S0304-0208(08)73398-XSuche in Google Scholar
[3] A. Kharazishvili, A characterization of rt-sets in Euclidean spaces (in Russian), Soobshch. Akad. Nauk Gruzin. SSR 86 (1977), no. 3, 537–540. Suche in Google Scholar
[4] A. Kharazishvili, Some properties of at-sets and ot-sets in a Hilbert space, Proc. A. Razmadze Math. Inst. 159 (2012), 147–151. Suche in Google Scholar
[5] A. Kharazishvili, On the cardinalities of at-sets in a real Hilbert space, Georgian Math. J. 22 (2015), no. 2, 259–263. 10.1515/gmj-2015-0014Suche in Google Scholar
[6] A. Kharazishvili and T. Tetunashvili, On some combinatorial problems concerning geometrical realizations of finite and infinite families of sets, Georgian Math. J. 15 (2008), no. 4, 665–675. 10.1515/GMJ.2008.665Suche in Google Scholar
[7] A. Kharazishvili and T. Tetunashvili, Combinatorial properties of families of sets and Euler-Venn diagrams, Proc. A. Razmadze Math. Inst. 146 (2008), 115–119. Suche in Google Scholar
[8]
T. Tetunashvili,
On the structure of constituents of finite independent families of convex bodies in
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On absolutely Baire nonmeasurable functions
- Existence of special rainbow triangles in weak geometries
- Images of Bernstein sets via continuous functions
- Square-integrable representations and multipliers
- Semigroups of pathological sets
- Points of density and ideals of subsets of ℕ
- On Kharazishvili type measures in infinite-dimensional Polish vector spaces
- Families of symmetric Cantor sets from the category and measure viewpoints
- On the Gitik–Shelah theorem
- On equidistant lines of given line configurations
- On convergence of sequences of functions possessing closed graphs
- On combinatorial and set-theoretical aspects of some finite and infinite point sets
- On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
- Automorphism groups of mono-unary algebras and CH
- On topologies related to the extension of the Lebesgue measure
- An abstract formulation of a theorem of Sierpiński on the nonmeasurable sum of two measure zero sets
- Local affine selections of convex set-valued functions
- On orbits without the Baire property
- Mann iteration process for monotone nonexpansive mappings with a graph
- Mixing coded systems
- Methods of comparison of families of real functions in porosity terms
Artikel in diesem Heft
- Frontmatter
- On absolutely Baire nonmeasurable functions
- Existence of special rainbow triangles in weak geometries
- Images of Bernstein sets via continuous functions
- Square-integrable representations and multipliers
- Semigroups of pathological sets
- Points of density and ideals of subsets of ℕ
- On Kharazishvili type measures in infinite-dimensional Polish vector spaces
- Families of symmetric Cantor sets from the category and measure viewpoints
- On the Gitik–Shelah theorem
- On equidistant lines of given line configurations
- On convergence of sequences of functions possessing closed graphs
- On combinatorial and set-theoretical aspects of some finite and infinite point sets
- On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
- Automorphism groups of mono-unary algebras and CH
- On topologies related to the extension of the Lebesgue measure
- An abstract formulation of a theorem of Sierpiński on the nonmeasurable sum of two measure zero sets
- Local affine selections of convex set-valued functions
- On orbits without the Baire property
- Mann iteration process for monotone nonexpansive mappings with a graph
- Mixing coded systems
- Methods of comparison of families of real functions in porosity terms
