On the intrinsic topology and some related ideals of 𝐶(𝑋)-Reference-Cited by-同舟云学术

On the intrinsic topology and some related ideals of 𝐶(𝑋)

Published:1985 Issue:1 Volume:93 Page:179-184
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Karamzadeh O. A. S.,Rostami M.

Abstract

The above topology is defined and studied on C ( X ) C(X) , the ring of real-valued continuous functions on a completely regular Hausdorff space X X . The minimal ideals and the socle of C ( X ) C(X) are characterized via their corresponding z z -filters. We observe that these ideals are z z -ideals and X X is discrete if and only if the socle of C ( X ) C(X) is a free ideal. It is also shown that for a class of topological spaces, containing all P P -spaces, the family C k ( X ) {C_k}(X) of functions with compact support is identical with the intersection of the free maximal ideals of C ( X ) C(X) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1985-093-01/S0002-9939-1985-0766552-9/S0002-9939-1985-0766552-9.pdf

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