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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.
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