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Rigid extensions of $ℓ$ -groups of continuous functions

Michelle L. Knox; Warren Wm. McGovern — 2008

Czechoslovak Mathematical Journal

Let $C (X, ℤ)$ , $C (X, ℚ)$ and $C (X)$ denote the $ℓ$ -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space $X$ , respectively. Characterizations are given for the extensions $C (X, ℤ) \leq C (X, ℚ) \leq C (X)$ to be rigid, major, and dense.

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