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Pasting topological spaces at one point

Ali Rezaei Aliabad — 2006

Czechoslovak Mathematical Journal

Let { X α } α Λ be a family of topological spaces and x α X α , for every α Λ . Suppose X is the quotient space of the disjoint union of X α ’s by identifying x α ’s as one point σ . We try to characterize ideals of C ( X ) according to the same ideals of C ( X α ) ’s. In addition we generalize the concept of rank of a point, see [9], and then answer the following two algebraic questions. Let m be an infinite cardinal. (1) Is there any ring R and I an ideal in R such that I is an irreducible intersection of m prime ideals? (2) Is there...

Fixed-place ideals in commutative rings

Ali Rezaei AliabadMehdi Badie — 2013

Commentationes Mathematicae Universitatis Carolinae

Let I be a semi-prime ideal. Then P Min ( I ) is called irredundant with respect to I if I P P Min ( I ) P . If I is the intersection of all irredundant ideals with respect to I , it is called a fixed-place ideal. If there are no irredundant ideals with respect to I , it is called an anti fixed-place ideal. We show that each semi-prime ideal has a unique representation as an intersection of a fixed-place ideal and an anti fixed-place ideal. We say the point p β X is a fixed-place point if O p ( X ) is a fixed-place ideal. In this situation...

Rings of continuous functions vanishing at infinity

Ali Rezaei AliabadF. AzarpanahM. Namdari — 2004

Commentationes Mathematicae Universitatis Carolinae

We prove that a Hausdorff space X is locally compact if and only if its topology coincides with the weak topology induced by C ( X ) . It is shown that for a Hausdorff space X , there exists a locally compact Hausdorff space Y such that C ( X ) C ( Y ) . It is also shown that for locally compact spaces X and Y , C ( X ) C ( Y ) if and only if X Y . Prime ideals in C ( X ) are uniquely represented by a class of prime ideals in C * ( X ) . -compact spaces are introduced and it turns out that a locally compact space X is -compact if and only if every...

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