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boundedness in a topological vector space generalizes boundedness in a normed space∗ PrimeFan† 2013-03-21 19:47:42 Boundedness in a topological vector space is a generalization of boundedness in a normed space. Suppose (V, k·k) is a normed vector space over C, and suppose B is bounded in the sense of the parent entry. Then for the unit ball B1 (0) = {v ∈ V : kvk < 1} there exists some λ ∈ C such that B ⊆ λB1 (0). Using this result, it follows that B ⊆ B|λ| (0). ∗ hBoundednessInATopologicalVectorSpaceGeneralizesBoundednessInANormedSpacei created: h2013-03-21i by: hPrimeFani version: h37459i Privacy setting: h1i hResulti h46-00i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1