• Journal for History of Mathematics
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• v.18 no.4
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• pp.113-124
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• 2005

For a Tychonoff space X, C(X) is a Riesz-space. It is well known that C(X) is order-Cauchy complete if and only if X is a quasi~F space and that if X is a compact space and QF(X) is a minimal quasi-F cover of X, then the order- Cauchy completion of C(X) is isomorphic to C(QF(X)). In this paper, we investigate motivations and historical backgrounds of the definition for quasi-spaces and the construction for minimal quasi-F covers.