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ON TOPOLOGICAL EQ-ALGEBRAS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 15، شماره 6، بهمن و اسفند 2018، صفحه 145-158 اصل مقاله (358.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.4372 | ||
| نویسندگان | ||
| Jiang Yang1؛ Xiao Long Xin* 1؛ Peng Fei He2 | ||
| 1School of Mathematics, Northwest University, Xi'an,710127, China | ||
| 2School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, China | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Topological $EQ$-algebra؛ System of filters؛ Cauchy sequence | ||
| مراجع | ||
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