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

摘要： 拓扑结构是逻辑代数中一个重要的研究内容。为描述Fuzzy蕴涵代数的拓扑结构，利用滤子诱导的同余关系在FI代数上构造一致结构和一致拓扑，证明了导出的一致拓扑空间是不连通的、零维的、局部紧的、完全正则的第一可数空间，是[T0]空间当且仅当诱导它的滤子为{1}，且FI代数中的蕴涵运算关于导出的一致拓扑是连续的。此外，讨论了商空间的性质。这对从拓扑层面去揭示FI代数的内部结构具有促进作用。

关键词: FI代数, 滤子, 一致拓扑