Function lattices and compactifications

• Alaste, Tomi Matias ^[1]
  1. [1] University of Oulu

     University of Oulu

     Oulu, Finlandia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 2, 2014, págs. 183-202
• Idioma: inglés
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• Resumen

  • 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.