A Note on Separating Function Sets
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We study separating function sets. We find some necessary and sufficient conditions for C p (X) or C p 2 (X) to have a point-separating subspace that is a metric space with certain nice properties. One of the corollaries to our discussion is that for a zero-dimensional X, C p (X) has a discrete point-separating space if and only if C p 2 (X) does.
Keywords and phrasesCp(X) discrete space point-separating set spread i-weight σ-product
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