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Let X be a completely regular Hausdorff topological space. It is shown that the ring of real valued continuous functions is po-coherent (in the sense of F. Wehrung) if and only if X is basically disconnected.
The author wishes to thank his Ph.D. adviser Professor Boris Lavricˇ for presenting this problem, all the encouragement and careful reading of the text.
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A po-COHERENT RING?