Function lattices and compactifications

Tomi Matias Alaste

Abstract

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 ℓ∞(X) containing the constant functions, then our construction gives a representation of the spectrum of A as a space of filters on X.


Keywords

Function lattice; F-filter; F-ultrafilter; spectrum

Subject classification

46E05; 54D80; 54D35.

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References

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