๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Operation continuity of effect algebras

โœ 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.

โœฆ Synopsis


In this paper, we prove that the operations โŠ• 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 โˆจ and โˆง are also continuous with respect to their ideal topology.


๐Ÿ“œ SIMILAR VOLUMES


Automatic Continuity of Lipschitz Algebr
โœ B. Pavlovic ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 980 KB

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