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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 \(U\).

MSC:

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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