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An extension of a theorem of Bessaga


Author: Charles A. Riley
Journal: Proc. Amer. Math. Soc. 48 (1975), 231-235
MSC: Primary 58B05; Secondary 46A15, 57A17
DOI: https://doi.org/10.1090/S0002-9939-1975-0402797-9
MathSciNet review: 0402797
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Abstract: In [1], C. Bessaga has shown that if $ X$ is a linear topological space admitting a weak incomplete norm $ w$ and $ A \subset X$ is closed in the $ w$-completion of $ X$, then $ A$ is negligible in $ X$. The present paper establishes this result in a space admitting a weak incomplete linear metric.


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

  • [1] C. Bessaga, Negligible sets in linear topological spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 16 (1968), 117-119. MR 37 #1946. MR 0226356 (37:1946)
  • [2] R. T. Ives, Semi-convexity and locally bounded spaces, Ph.D. Thesis, University of Washington, Seattle, Wash., 1957.
  • [3] V. L. Klee, Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10-43. MR 14, 989. MR 0054850 (14:989d)
  • [4] -, Shrinkable neighborhoods in Hausdorff linear spaces, Math. Ann. 141 (I960), 281-285. MR 24 #A1003. MR 0131149 (24:A1003)
  • [5] C. A. Riley, Negligibility in nonlocally convex spaces, Proc. Amer. Math. Soc. 41 (1973), 619-624. MR 0322878 (48:1239)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0402797-9
Keywords: Negligibility, shrinkable set, paranorm
Article copyright: © Copyright 1975 American Mathematical Society

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