Small sets in convex geometry and formal independence over ZFC
To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets 𝒥 (S) which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.469 |
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| _version_ | 1832549838679441408 |
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| author | Menachem Kojman |
| author_facet | Menachem Kojman |
| author_sort | Menachem Kojman |
| collection | DOAJ |
| description | To each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets 𝒥 (S) which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations. |
| format | Article |
| id | doaj-art-104b3dccb2b64e5d9fd3c2c6909588ad |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-104b3dccb2b64e5d9fd3c2c6909588ad2025-02-03T06:08:19ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005546948810.1155/AAA.2005.469Small sets in convex geometry and formal independence over ZFCMenachem Kojman0Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva 84105, IsraelTo each closed subset S of a finite-dimensional Euclidean space corresponds a σ-ideal of sets 𝒥 (S) which is σ-generated over S by the convex subsets of S. The set-theoretic properties of this ideal hold geometric information about the set. We discuss the relation of reducibility between convexity ideals and the connections between convexity ideals and other types of ideals, such as the ideals which are generated over squares of Polish space by graphs and inverses of graphs of continuous self-maps, or Ramsey ideals, which are generated over Polish spaces by the homogeneous sets with respect to some continuous pair coloring. We also attempt to present to nonspecialists the set-theoretic methods for dealing with formal independence as a means of geometric investigations.http://dx.doi.org/10.1155/AAA.2005.469 |
| spellingShingle | Menachem Kojman Small sets in convex geometry and formal independence over ZFC Abstract and Applied Analysis |
| title | Small sets in convex geometry and formal independence over ZFC |
| title_full | Small sets in convex geometry and formal independence over ZFC |
| title_fullStr | Small sets in convex geometry and formal independence over ZFC |
| title_full_unstemmed | Small sets in convex geometry and formal independence over ZFC |
| title_short | Small sets in convex geometry and formal independence over ZFC |
| title_sort | small sets in convex geometry and formal independence over zfc |
| url | http://dx.doi.org/10.1155/AAA.2005.469 |
| work_keys_str_mv | AT menachemkojman smallsetsinconvexgeometryandformalindependenceoverzfc |