关键词: FI代数, 滤子, 一致拓扑

Abstract: Topological structure is an important area of research in logic algebras. Based on the congruence induced by filters in fuzzy implication algebras, uniformities and uniform topologies are established to describe their topological structure. These topological spaces are disconnected, zero-dimensional, locally compact, completely regular and first-countable spaces, and which is a [T0] space if and only if the filter is equal to {1}. Moreover, it is proven that the implication operation is continuous in the uniform topological spaces. Finally, some properties of the uniform topology on the quotient FI algebra under the equivalence relation induced by a filter are also discussed. The results of this paper have a positive role to reveal internal structure of FI algebras on topological level.

Key words: FI algebra, filter, uniform topology