CONNECTIONS BETWEEN C(X) AND C(Y), WHERE Y IS A SUBSPACE OF X

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ALIABAD A.R.; BADIE M.

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ISSN: 2588-4824

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Paper Information

Journal: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY Year:2011 | Volume:37 | Issue:4 Page(s): 109-126

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Title

CONNECTIONS BETWEEN C(X) AND C(Y), WHERE Y IS A SUBSPACE OF X

Author(s)

ALIABAD A.R. | BADIE M. | Issue Writer Certificate

Keywords

Z-FILTER

PRIME Z-IDEAL

PRIME ZO-IDEAL

P-SPACE

QUASI P-SPACE

F-SPACE

CC-SPACE

Gδ-POINT

Abstract

In this paper, we introduce a method by which we can find a close connection between the set of primez-ideals of C(X) and the same of C (Y), for some special subset Y of X. For instance, if Y=Coz (f) for some fÎC (X), then there exists a oneto-one correspondence between the set of primez-ideals of C (Y) and the set of primez-ideals of C (X) not containing f. Moreover, considering these relations, we obtain some new characterizations of classical concepts in the context of C (X). For example, X is an F-SPACE if and only if the extension F: bY®bX of the identity map i: Y ® X is one-to-one, for each z-embedded subspace Y of X. Supposing p is a non-isolated Gd-point in X and Y=X \ {p}, we prove that Mp (X) contains no non-trivial maximal z-ideal if and only if pÎ bX is a quasi P-point if and only if each point of bY\ Y is a P-point with respect to Y.

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APA: Copy

ALIABAD, A.R., & BADIE, M.. (2011). CONNECTIONS BETWEEN C(X) AND C(Y), WHERE Y IS A SUBSPACE OF X. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 37(4), 109-126. SID. https://sid.ir/paper/628072/en

Vancouver: Copy

ALIABAD A.R., BADIE M.. CONNECTIONS BETWEEN C(X) AND C(Y), WHERE Y IS A SUBSPACE OF X. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY[Internet]. 2011;37(4):109-126. Available from: https://sid.ir/paper/628072/en

IEEE: Copy

A.R. ALIABAD, and M. BADIE, “CONNECTIONS BETWEEN C(X) AND C(Y), WHERE Y IS A SUBSPACE OF X,” BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol. 37, no. 4, pp. 109–126, 2011, [Online]. Available: https://sid.ir/paper/628072/en

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