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• # Artykuł - szczegóły

## Open Mathematics

2013 | 11 | 12 | 2176-2181

## The combinatorial derivation and its inverse mapping

EN

### Abstrakty

EN
Let G be a group and P G be the Boolean algebra of all subsets of G. A mapping Δ: P G → P G defined by Δ(A) = {g ∈ G: gA ∩ A is infinite} is called the combinatorial derivation. The mapping Δ can be considered as an analogue of the topological derivation d: P X→ P X, A ↦ A d, where X is a topological space and A d is the set of all limit points of A. We study the behaviour of subsets of G under action of Δ and its inverse mapping ∇. For example, we show that if G is infinite and I is an ideal in P G such that Δ(A) ∈ I and ∇(A) ⊆ I for each A ∈ I then I = P G.

EN

2176-2181

wydano
2013-12-01
online
2013-10-08

### Twórcy

autor
• Kyiv University

### Bibliografia

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