Insertion, approximation, and extension of real-valued functions

Blair, Robert L.; Swardson, Mary Anne

doi:10.1090/S0002-9939-1985-0766550-5

Insertion, approximation, and extension of real-valued functions
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by Robert L. Blair and Mary Anne Swardson

Proc. Amer. Math. Soc. 93 (1985), 169-175

DOI: https://doi.org/10.1090/S0002-9939-1985-0766550-5

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Abstract:

For a uniformly closed vector lattice $V$ of real-valued functions on a set $X$, necessary and sufficient conditions are obtained for insertion (or "strict insertion") of some member of $V$ between two arbitrary real-valued functions on $X$. These conditions quickly yield known insertion, approximation, and extension theorems for real-valued functions.

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Über halbstetige und unstetige Funktionen

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