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_2ordered, 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  19740310

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

OAIPMH Set 
Faculty of Science and Engineering
