An order-theoretic description of Marinescu spaces
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- by W. A. Feldman and J. F. Porter PDF
- Proc. Amer. Math. Soc. 41 (1973), 602-608 Request permission
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
- Ralph DeMarr, Partially ordered linear spaces and locally convex linear topological spaces, Illinois J. Math. 8 (1964), 601–606. MR 171157
- Hans Jarchow, Marinescu-Räume, Comment. Math. Helv. 44 (1969), 138–163 (German). MR 250019, DOI 10.1007/BF02564519
- G. Marinescu, Espaces vectoriels pseudotopologiques et théorie des distributions, Hochschulbücher für Mathematik, Band 59, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963 (French). MR 0166605
- Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
Additional Information
- © Copyright 1973 American Mathematical Society
- 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