- Tytuł:
- Fractal sets satisfying the strong open set condition in complete metric spaces
- Autorzy:
- Goodman, G. S.
- Powiązania:
- https://bibliotekanauki.pl/articles/952847.pdf
- Data publikacji:
- 2008
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
address
Baire category
fractal
scaling function
scaling operator
strong open set condition - Opis:
- Let K be a Hutchinson fractal in a complete metric space X, invariant under the action S of the union of a finite number of Lipschitz contractions. The Open Set Condition states that X has a non-empty subinvariant bounded open subset V, whose images under the maps are disjoint. It is said to be strong if V meets K. We show by a category argument that when K ⊄ V and the restrictions of the contractions to V are open, the strong condition implies that [formula] termed the core of V, is non-empty. In this case, it is an invariant, proper, dense, subset of K, made up of points whose addresses are unique. Conversely, [formula] implies the SOSC, without any openness assumption.
- Źródło:
-
Opuscula Mathematica; 2008, 28, 4; 463-470
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł