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Hadwin, D · 2004

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math.FA 1

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Additive Local Multiplications and zero-preserving maps on $C(X)$

math.FA · 2019-08-15 · conditional · novelty 7.0

For a compact Hausdorff space X, every additive zero-preserving map on C_R(X) is a multiplication exactly when X has no isolated points, and every additive local multiplication on C(X) is a multiplication exactly when no nonempty open F-sigma subset of X is an F-space.

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  • Additive Local Multiplications and zero-preserving maps on $C(X)$ math.FA · 2019-08-15 · conditional · none · ref 8

    For a compact Hausdorff space X, every additive zero-preserving map on C_R(X) is a multiplication exactly when X has no isolated points, and every additive local multiplication on C(X) is a multiplication exactly when no nonempty open F-sigma subset of X is an F-space.