ON TOPOLOGICAL EQ-ALGEBRAS
نویسندگان
1 School of Mathematics, Northwest University, Xi'an,710127, China
2 School of Mathematics, Northwest University, Xi'an,710127, China
3 School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, China
doi
10.22111/ijfs.2018.4372چکیده
In this paper, by using a special family of filters $\mathcal{F}$ on an EQ-algebra $E$, we construct a topology $\mathcal{T}_{\mathcal{\mathcal{F}}}$ on $E$ and show that $(E,\mathcal{T}_{\mathcal{F}})$ is a topological EQ-algebra. First of all, we give some properties of topological EQ-algebras and investigate the interaction of topological EQ-algebras and quotient topological EQ-algebras. Then we obtain the form of closure of each subset and show that $(E,\mathcal{T}_{\mathcal{F}})$ is a zero-dimensional space. Finally, we introduce the concept of convergence of sequences on topological EQ-algebras and give a condition under which the limit of a sequence is unique.
