A topology on categorical algebras

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.

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,...

Completing Categorical Algebras

Let Σ be a ranked set. A categorical Σ-algebra, cΣa for short, is a small category C equipped with a functor σC : C n //C, for each σ ∈ Σn, n ≥ 0. A continuous categorical Σ-algebra is a cΣa which has an initial object and all colimits of ω-chains, i.e., functors N //C; each functor σC preserves colimits of ω-chains. (N is the linearly ordered set of the nonnegative integers considered as a cat...

A Categorical Equivalence for Product Algebras

Net Spaces in Categorical Topology

In the paper we introduce the notion of S-nets, S a non-empty construct , as a generalization of the usual nets. S-net spaces and continuous maps between them are then deened in a natural way. For S-net spaces we introduce a number of axioms and study the categories obtained. We nd some topological and cartesian closed categories of S-net spaces and describe their relations to certain known top...