Function lattices and compactifications
Keywords:Function lattice, F-filter, F-ultrafilter, spectrum
Let F be a lattice of real-valued functions on a non-empty set X such that F contains the constant functions. Using certain filters on X determined by F, we construct a compact Hausdorff topological space δX with the property that every bounded member of F extends to δX and these extensions form a dense subspace of C(δX). If A is any C*-subalgebra of â„“âˆž(X) containing the constant functions, then our construction gives a representation of the spectrum of A as a space of filters on X.
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