Some lattices of continuous functions on locally compact spaces. (English) Zbl 1161.26001

For a locally compact Hausdorff space \(U\), which is not compact, the author introduces the lattice \(L(U)\), which is the family of all continuous real-valued functions on \(U\) such that for each \(f\in L(U)\) there is a nonzero number \(p\) (depending on \(f\)) for which \(f-p\) vanishes at infinity. For \(L(U)\) is proved that \(L(U)\), as a lattice alone, characterizes the locally compact space \(U\).


26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54D30 Compactness
54D45 Local compactness, \(\sigma\)-compactness
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