مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Information Seminar Paper

Title

C(X) VERSUS CC(X)

Author(s)

 KARAMZADEH O.A.S.

Pages

  -

Abstract

 LET CC(X) (RESP. CF(X)) DENOTE THE SUBRING OF C(X) CONSISTING OF FUNCTIONS WITH COUNTABLE (RESP.FINITE) IMAGE AND CF(X) BE THE SOCLE OF C(X). IF X IS ANY TOPOLOGICAL SPACE THERE IS A ZERO-DIMENSIONAL SPACEY SUCH THAT CC(X) @ CC(Y). WE CHARACTERIZE SPACES X WITH C*(X) = CC(X), WHICH GENERALIZES A CELEBRATED RESULT DUE TO RUDIN, PELCZYNNSKI AND SEMADENI. TWO ZERO-DIMENSIONAL COMPACT SPACES X, Y ARE HOMEOMORPHIC IF AND ONLY IF CC(X) @ CC(Y) (RESP. CF(X) @ CF(Y)). THE WELL-KNOWN ALGEBRAIC PROPERTY OF C(X), WHERE X IS REALCOMPACT, IS EXTENDED TO CC(X). IN CONTRAST TO THE FACT THAT CF(X) IS NEVER PRIME IN C(X), WE CHARACTERIZE SPACES X FOR WHICH CF(X) IS A PRIME IDEAL IN CC(X). IT IS OBSERVED FOR THESE SPACES, CC(X) COINCIDES WITH ITS OWN SOCLE (A FACT, WHICH IS NEVER TRUE FOR C(X)). FINALLY, WE SHOW THAT A SPACE X IS THE ONE-POINT COMPACTIFICATION OF A DISCRETE SPACE IF AND ONLY IF CF(X) IS A UNIQUE PROPER ESSENTIAL IDEAL IN CF(X), SEE [9], [10]. A SIMILAR CHARACTERIZATION, AS THE GELFAND-KOLMOGOROFF THEOREM FOR THE MAXIMAL IDEALS IN C(X), IS GIVEN FOR THE MAXIMAL IDEALS OF CC(X), SEE [4]. THE SUBALGEBRA LC(X) = {¦ Í C(X): C¦ = X} OF C(X), WHERE C¦ IS THE UNION OF ALL OPEN SUBSETS U Í  X SUCH THAT |¦ (U)| £ À0, WHICH IS CC(X) Í  LC(X)  Í C(X), SEE [13].

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    • Cite

    APA: Copy

    KARAMZADEH, O.A.S.. (). . . SID. https://sid.ir/paper/938530/en

    Vancouver: Copy

    KARAMZADEH O.A.S.. . . Available from: https://sid.ir/paper/938530/en

    IEEE: Copy

    O.A.S. KARAMZADEH, “,” presented at the . , [Online]. Available: https://sid.ir/paper/938530/en

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