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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A vector lattice topology and function space representation
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by W. A. Feldman and J. F. Porter PDF
Trans. Amer. Math. Soc. 235 (1978), 193-204 Request permission

Abstract:

A locally convex topology is defined for a vector lattice having a weak order unit and a certain partition of the weak order unit, analogous to the order unit topology. For such spaces, called β€œorder partition spaces,” an extension of the classical Kakutani theorem is obtained: Each order partition space is lattice isomorphic and homeomorphic to a dense subspace of ${C_c}(X)$ containing the constant functions for some locally compact X, and conversely each such ${C_c}(X)$ is an order partition space. $({C_c}(X)$ denotes all continuous real-valued functions on X with the topology of compact convergence.) One consequence is a lattice-theoretic characterization of ${C_c}(X)$ for X locally compact and realcompact. Conditions for an M-space to be an order partition space are provided.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 235 (1978), 193-204
  • MSC: Primary 46E05; Secondary 46A40, 54C40
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0463897-8
  • MathSciNet review: 0463897