## 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 βorder partition spaces,β 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