Conditions on Normal Spaces of Finite Rank That Guarantee C(X) is SV |
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Authors: | Suzanne Larson |
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Institution: | 1. Loyola Marymount University, Los Angeles, California, USAslarson@lmu.edu |
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Abstract: | An f-ring A is an SV f-ring if for every minimal prime ?-ideal P of A, A/P is a valuation domain. A topological space X is an SV space if C(X) is an SV f-ring. For normal spaces, several conditions are shown to guarantee the space is an SV space. For example, a normal space of finite rank for which the closure of the set of points of rank greater than 1 is an F-subspace, is an SV space. For normal spaces of rank 2, a characterization of SV spaces is given. |
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Keywords: | f-rings Rank of a maximal ideal Rings of continuous functions SV f-ring SV space |
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