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Proceedings of the American Mathematical Society

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Linear extensions of convex subsets


Author: Hideyuki Fujihira
Journal: Proc. Amer. Math. Soc. 89 (1983), 130-132
MSC: Primary 52A07; Secondary 46A55
MathSciNet review: 706525
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Abstract: We give conditions for linear extensions of closed convex subsets of topological vector spaces to be closed.


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

  • [1] Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
  • [2] J. L. Kelley and Isaac Namioka, Linear topological spaces, With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR 0166578
  • [3] N. Bourbaki, Éléments de mathématique, Espaces vectoriels topologiques, Chap. 3-5, Hermann, Paris, 1955.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0706525-3
Keywords: Convex sets, linear extensions, radial kernels, barrelled spaces
Article copyright: © Copyright 1983 American Mathematical Society