- 作者: 郭仁泰;石輝然
- 作者服務機構: 國立中興大學應用數學系
- 中文摘要: 討論某些定義在一自由半群上的半序所衍生出的拓樸的性質。特別地,我們考慮 , , , 和 等半序。我們獲得同態映射對由 , , 和 等半序所衍生出的拓樸而言是連續函數,而對 所衍生之拓樸是連續函數的充分必要為:對於所有的定母 x 和 y , lg(f(x)) = lg(f(y))同時我們獲得拓樸自由半群的半序之特徵化性質。最後,我們討論對於任何語言E,OK (E),OH (E),CK (E),和CH (E)的正規性。
- 英文摘要: We discuss the properties of topologies by some partial orders on a free monoid. Especially, weconsider the partial orders , , and . We obtain that a homomorphism is continuous with respectto the topologies induced by , , and , and a necessary and sufficient condition for a homomorphismto be continuous with respect to the topology induced by is that, for any alphabets x and y, lg(f(x)) =lg (f(y)). Also, we obtain a characterization of topological monoids by the properties of partial orders.Finally, we discuss the regularity of OK (E), OH (E), CK (E) and CH (E) for any language E.
- 中文關鍵字: code; Partial order; free monoid; regular language; topological monoid
- 英文關鍵字: --