Order Topology and Frink Ideal Topology of Effect Algebras

Order Topology and Frink Ideal Topology of Effect Algebras

In this paper we prove the following conclusions: (1). If E is a complete atomic lattice effect algebra, then E is (o)-continuous ⇔ E is order-topological ⇔ E is a totally order-disconnected ⇔ E is algebraic. (2). If E is a complete atomic distributive lattice effect algebra, then its Frink ideal topology τid is Hausdorff topology and is finer than its order topology τo, and τid = τo ⇔ 1 is fin...

Inverse topology in BL-algebras

In this paper, we introduce Inverse topology in a BL-algebra A and prove the set of all minimal prime filters of A, namely Min(A) with the Inverse topology is a compact space, Hausdorff, T0  and T1-Space. Then, we show that Zariski topology on Min(A) is finer than the Inverse topology on Min(A). Then, we investigate what conditions may result in the equivalence of these two topologies. Finally,...

A topology on BCK-algebras via left and right stabilizers

In this paper, we use the left(right) stabilizers of a BCKalgebra (X, &lowast, 0) and produce two basis for two different topologies. Then we show that the generated topological spaces by these basis are Bair, connected, locally connected and separable. Also we study the other properties of these topological spaces.

Axioms, Algebras and Topology

Axiomatic theories provide a very general means for specifying the logical properties of formal concepts. From the axiomatic point of view, it is symbolic formulae and the logical relations between them — especially the entailment relation — that form the primary subject of interest. The vocabulary of concepts of any theory can be interpreted in terms of a domain of entities, which exemplify pr...

Operator algebras and topology