Operation continuity of effect algebras
โ Scribed by Zhi-Jian Yu; Jun-De Wu; Min-Hyung Cho
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 218 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
โฆ Synopsis
In this paper, we prove that the operations โ and of effect algebras are continuous with respect to their ideal topology, and if the effect algebras are lattice effect algebras, then under some conditions, the lattice operations โจ and โง are also continuous with respect to their ideal topology.
๐ SIMILAR VOLUMES
For a compact metric space \((K, d), \alpha \in(0,1]\) and \(f \in C(K)\), let \(p_{x}(f)=\) \(\sup \left\{|f(t)-f(s)| d(t, s)^{x}: t, s \in K\right\}\). The set \(\operatorname{Lip}_{x}(K, d)=\left\{f \in C(K): p_{x}(f)<\infty\right\}\) with the norm \(\|f\|_{x}=|f|_{\kappa}+p_{x}(f)\) is a Banach