Abstract
Orrin Frink showed that the real-valued functions over a Tychonoff space X which may be continuously extended to ω ( Z ) \omega (\mathcal {Z}) , the Wallman-type compactification associated with a normal base Z \mathcal {Z} for X, are those which are Z \mathcal {Z} -uniformly continuous Let Z \mathcal {Z} be a delta normal base on a Tychonoff space X, and let η ( Z ) \eta (\mathcal {Z}) be the corresponding Z \mathcal {Z} -realcompactification of X. In this note we show that countable Z \mathcal {Z} -uniform continuity is a sufficient but not a necessary condition for continuously extending real-valued functions over X to η ( Z ) \eta (\mathcal {Z}) .
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