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An order-theoretic description of Marinescu spaces

Authors: W. A. Feldman and J. F. Porter
Journal: Proc. Amer. Math. Soc. 41 (1973), 602-608
MSC: Primary 46A15; Secondary 54A20
MathSciNet review: 0328528
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Abstract: It is shown that any inductive limit $ E$ in the category of convergence spaces of real locally convex topological vector spaces (i.e., any Marinescu space) can be embedded in a partially ordered vector space so that convergence in $ E$ can be characterized as an order-theoretic convergence. The order-theoretic convergence in question is a modification of classical order convergence.

References [Enhancements On Off] (What's this?)

  • [1] Ralph DeMarr, Partially ordered linear spaces and locally convex linear topological spaces, Illinois J. Math. 8 (1964), 601–606. MR 0171157
  • [2] Hans Jarchow, Marinescu-Räume, Comment. Math. Helv. 44 (1969), 138–163 (German). MR 0250019
  • [3] G. Marinescu, Espaces vectoriels pseudotopologiques et théorie des distributions, Hochschulbücher für Mathematik, Band 59, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963 (French). MR 0166605
  • [4] Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731

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Keywords: Convergence space, Marinescu space, partial order, order-theoretic convergence
Article copyright: © Copyright 1973 American Mathematical Society