“School of Mathematics”
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| Paper IPM / M / 737 |
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We prove that C∞(X) is an ideal in C(X) if and only if every open locally compact subset of X is bounded. In particular, if X is a locally compact Hausdorff space, C∞ (X) is an ideal of C(X) if and only if X is a pseudocompact space. It is shown that the existence of some special functions in C∞ (X) causes C∞(X) not to be an ideal of C(X). Finally we will characterize the spaces X for which C∞(X) and CK(X), or Cψ (X), coincide.
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