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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1973-0328528-7
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.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0328528-7
Keywords: Convergence space, Marinescu space, partial order, order-theoretic convergence
Article copyright: © Copyright 1973 American Mathematical Society