| 1. | Every finite-dimensional normed space over or is a Banach space.
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| 2. | Thus becomes a complex normed space with open unit ball.
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| 3. | Normed spaces for which the map ? is a bijection are called reflexive.
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| 4. | Any linear operator defined on a finite-dimensional normed space is bounded.
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| 5. | Every inner product space is also a normed space.
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| 6. | The cartesian product of two normed spaces is not canonically equipped with a norm.
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| 7. | As a complete normed space, Hilbert spaces are by definition also Banach spaces.
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| 8. | And give rise to isomorphic normed spaces.
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| 9. | X " is a normed space the sets may be taken to be convex.
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| 10. | Incidentally, by the Kuratowski embedding any metric space is isometric to a subset of a normed space.
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