A vector lattice topology and function space representation
Authors:
W. A. Feldman and J. F. Porter
Journal:
Trans. Amer. Math. Soc. 235 (1978), 193204
MSC:
Primary 46E05; Secondary 46A40, 54C40
MathSciNet review:
0463897
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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 ``order 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 containing the constant functions for some locally compact X, and conversely each such is an order partition space. denotes all continuous realvalued functions on X with the topology of compact convergence.) One consequence is a latticetheoretic characterization of for X locally compact and realcompact. Conditions for an Mspace to be an order partition space are provided.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197804638978
PII:
S 00029947(1978)04638978
Keywords:
Compact convergence,
function space,
topological Mspace,
vector lattice,
weak order unit
Article copyright:
© Copyright 1978 American Mathematical Society
