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