On topological BCI-algebras

Abstract

We introduce the notion of topological BCI-algebras (briefly, TBCI-algebras) andfind some properties of this structure. We give a characterization of a TBCI-algebra in terms of neighborhoods. We show that a TBCI-algebra X is Hausdorf if and only if {0} is closed in X. We give a filter base Ω generating a BCI-topology, and making a BCI-algebra X into a TBCI-algebra for which Ω is a fundamental system of neighborhoods of 0.