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Title Transcription
ショウ イソウ ジュンジョ クウカン ニツイテ
Title Alternative
On the Quotient Topological Ordered Spaces
File
language
eng
Author
Miwa, Takuo
Description
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.
Journal Title
Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
Volume
7
Start Page
37
End Page
42
ISSN
03709434
Published Date
1974-03-10
NCID
AN0010806X
Publisher
島根大学文理学部
Publisher Aalternative
The Faculty of Literature and Science, Shimane University
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Shimane University
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