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Article

Knox, Michelle L. ; McGovern, Warren Wm.
Rigid extensions of $\ell$-groups of continuous functions. (English). Czechoslovak Mathematical Journal, vol. 58 (2008), issue 4, pp. 993-1014
MSC: 06F20, 54C40, 54F65 | MR 2471161 | Zbl 1174.06341
Keywords:
rigid extension; major extension; archimedean extension; dense extension
Summary:
Let $C(X,\mathbb Z )$, $C(X,\mathbb Q )$ and $C(X)$ denote the $\ell $-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space $X$, respectively. Characterizations are given for the extensions $C(X,\mathbb Z )\leq C(X,\mathbb Q )\leq C(X)$ to be rigid, major, and dense.
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