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Add Real TVS trait to Weak topology on separable Hilbert space (#1748)
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spaces/S000021/properties/P000199.md

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---
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space: S000021
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property: P000087
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property: P000238
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value: true
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refs:
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- doi: 10.1016/B978-0-12-622760-4.X5000-6
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name: Handbook of Analysis and Its Foundations
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---
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$H$ with the weak topology is a topological vector space under
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addition. In particular, it is an abelian topological group.
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See 28.15 of {{doi:10.1016/B978-0-12-622760-4.X5000-6}}.

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