- Tytuł:
- On Ditkin sets
- Autorzy:
-
Muraleedharan, T.
Parthasarathy, K. - Powiązania:
- https://bibliotekanauki.pl/articles/967020.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- In the study of spectral synthesis S-sets and C-sets (see Rudin [3]; Reiter [2] uses the terminology Wiener sets and Wiener-Ditkin sets respectively) have been discussed extensively. A new concept of Ditkin sets was introduced and studied by Stegeman in [4] so that, in Reiter's terminology, Wiener-Ditkin sets are precisely sets which are both Wiener sets and Ditkin sets. The importance of such sets in spectral synthesis and their connection to the C-set-S-set problem (see Rudin [3]) are mentioned there. In this paper we study local properties, unions and intersections of Ditkin sets. (Warning: Usually in the literature "Ditkin set" means "C-set", but we follow the terminology of Stegeman.) Our results include: (i) if each point of a closed set E has a closed relative Ditkin neighbourhood, then E is a Ditkin set; (ii) any closed countable union of Ditkin sets is a Ditkin set; (iii) if $E_1 ∩ E_2$ is a Ditkin set, then $E_1 ∩ E_2$ is a Ditkin set if and only if $E_1$ and $E_2$ are Ditkin sets; and (iv) if $E_1, E_2$ are Ditkin sets with disjoint boundaries then $E_1 ∩ E_2$ is a Ditkin set.
- Źródło:
-
Colloquium Mathematicum; 1996, 69, 2; 271-274
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł