Families of separated sets
β Scribed by Stephen Watson
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 810 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
β¦ Synopsis
We characterize the possible subsets of P(K) which can arise as the family of separated subsets of a closed discrete subset 6 of a topological (Hausdorff, regular or normal) space.
π SIMILAR VOLUMES
Suppose that any t members (t 2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k 1Γt n 1&1Γt elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asympto
We use a lower bound on the number of small sets in an idea1 to show that for each unionclosed family of n sets there exists an element which belongs to at least of them, provided n is large enough.