| 1. | Let be a Banach space and be a normed vector space.
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| 2. | Isometrically isomorphic normed vector spaces are identical for all practical purposes.
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| 3. | This is the standard topology on any normed vector space.
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| 4. | The resulting normed vector space is, by definition,
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| 5. | They are generalizations of Banach spaces ( normed vector spaces that are norm ).
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| 6. | For this reason, not every scalar product space is a normed vector space.
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| 7. | Turning it into a normed vector space ( in fact a Banach space ).
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| 8. | Really, normed vector spaces are ubiquitous in many fields of science and engineering.
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| 9. | A vector space on which a norm is defined is called a normed vector space.
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| 10. | Let be a normed vector space.
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