Order Topology and Frink Ideal Topology of Effect Algebras

Details Order Topology and Frink Ideal Topology of Effect Algebras Order Topology and Frink Ideal Topology of Effect Algebras

2009-08-24

arxiv.org/abs/0908.3350v2

Physics

Mathematical Physics

Scientific paper

In this paper, the following results are proved: (1) $ $ If $E$ is a complete atomic lattice effect algebra, then $E$ is (o)-continuous iff $E$ is order-topological iff $E$ is totally order-disconnected iff $E$ is algebraic. (2) $ $ If $E$ is a complete atomic distributive lattice effect algebra, then its Frink ideal topology $\tau_{id}$ is Hausdorff topology and $\tau_{id}$ is finer than its order topology $\tau_{o}$, and $\tau_{id}=\tau_o$ iff 1 is finite iff every element of $E$ is finite iff $\tau_{id}$ and $\tau_o$ are both discrete topologies. (3) $ $ If $E$ is a complete (o)-continuous lattice effect algebra and the operation $\oplus$ is order topology $\tau_o$ continuous, then its order topology $\tau_{o}$ is Hausdorff topology. (4) $ $ If $E$ is a (o)-continuous complete atomic lattice effect algebra, then $\oplus$ is order topology continuous.

Affiliated with

Also associated with

No associations

Rating

Order Topology and Frink Ideal Topology of Effect Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Order Topology and Frink Ideal Topology of Effect Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Order Topology and Frink Ideal Topology of Effect Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-697383