| Autor: |
PROTASOV, I. V. |
| Předmět: |
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| Zdroj: |
Matematychni Studii; 2021, Vol. 55 Issue 1, p33-36, 4p |
| Abstrakt: |
A coarse structure ε on a set X is called finitary if, for each entourage E ∈ ε, there exists a natural number n such that E[x] < n for each x ∈ X. By a finitary approximation of a coarse structure E′, we mean any finitary coarse structure E such that E U E′. If E′ has a countable base and E[x] is finite for each x ∈ X then E′ has a cellular finitary approximation E such that the relations of linkness on subsets of (X; ε′) and (X; ε) coincide. This answers Question 6 from [8]: the class of cellular coarse spaces is not stable under linkness. We define and apply the strongest finitary approximation of a coarse structure. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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