An extension of a theorem of Bessaga
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- by Charles A. Riley PDF
- Proc. Amer. Math. Soc. 48 (1975), 231-235 Request permission
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
- C. Bessaga, Negligible sets in linear topological spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 117–119 (English, with Russian summary). MR 226356 R. T. Ives, Semi-convexity and locally bounded spaces, Ph.D. Thesis, University of Washington, Seattle, Wash., 1957.
- Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10–43. MR 54850, DOI 10.1090/S0002-9947-1953-0054850-X
- Victor Klee, Shrinkable neighborhoods in Hausdorff linear spaces, Math. Ann. 141 (1960), 281–285. MR 131149, DOI 10.1007/BF01360762
- Charles A. Riley, Negligibility in nonlocally convex spaces, Proc. Amer. Math. Soc. 41 (1973), 619–624. MR 322878, DOI 10.1090/S0002-9939-1973-0322878-6
Additional Information
- © Copyright 1975 American Mathematical Society
- 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