| 11. | Using the isometric embedding, it is customary to consider a normed space as a subset of its bidual.
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| 12. | The ! 0-normed space is studied in functional analysis, probability theory, and harmonic analysis.
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| 13. | Cells are defined in a normed space, commonly a two-dimensional Euclidean geometry, like a grid.
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| 14. | In particular, a normed space is an Hadamard space if and only if it is a Hilbert space.
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| 15. | The set of all vectors of norm less than one is called the unit ball of a normed space.
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| 16. | Hence, special uniformly continuous real-valued functions are essentially the restrictions of uniformly continuous functions on normed spaces.
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| 17. | Each infinite dimensional normed space X considered with the X ^ { \ star }-weak topology is not stereotype.
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| 18. | There exist normed spaces in any dimension for which certain sets of four equilateral points cannot be extended to any larger equilateral set
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| 19. | Being the dual of a normed space, the bidual is complete, therefore, every reflexive normed space is a Banach space.
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| 20. | Being the dual of a normed space, the bidual is complete, therefore, every reflexive normed space is a Banach space.
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