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タイトルヨミ
ショウ イソウ ジュンジョ クウカン ニツイテ
タイトル別表記
On the Quotient Topological Ordered Spaces
ファイル
言語
英語
著者
三輪 拓夫
内容記述(抄録等)
In the theory of general topology, the following theorem is well known(c. f. [2] or [4]) For a topological space X, and an equivalence relation R on X, if the quotient space X/R is Hausdorff, then R is closed in the product space X^2 . If the projection p of a space X onto the quotient space X/R is open, and R is closed in X^2, then X/R is a Hausdorff space. The analogy of this theorem in a topological ordered space has been obtained in the case where X is a compact ordered space (c. f. [9] Proposition 9). In this paper, we shall study the sufficient conditions for X/R to be T_2-ordered, and give some examples. For the problem of this kind, S. D. McCartan studied in [6] a particular quotient ordered space (that is, a quotient ordered space by a particular equivalence relation) which inherites some interesting properties of the domain ordered space.
The author wishes to express his gratitude to Professor Osamu Takenouchi for his helpful suggestions and encouragement in the preparation of this paper.
掲載誌名
島根大学文理学部紀要. 理学科編
7
開始ページ
37
終了ページ
42
ISSN
03709434
発行日
1974-03-10
NCID
AN0010806X
出版者
島根大学文理学部
出版者別表記
The Faculty of Literature and Science, Shimane University
資料タイプ
紀要論文
部局
島根大学
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