bounded metric meaning in Hindi

Examples

1. However, the discrete metric space is free in the category of bounded metric spaces and Lipschitz continuous maps, and it is free in the category of metric spaces bounded by 1 and short maps.
2. That is, any function from a discrete metric space to another bounded metric space is Lipschitz continuous, and any function from a discrete metric space to another metric space bounded by 1 is short.
3. The "'Kuratowski WojdysB
   awski "'theorem states that every bounded metric space " X " is isometric to a convex subset of some Banach space . ( N . B . the image of this embedding is closed in the convex subset, not necessarily in the Banach space . ) Here we use the isometry
4. Furthermore, \ delta _ X \ colon x \ mapsto d _ x, where d _ x ( p ) : = d ( x, p ) \,, is an isometric embedding of X into \ operatorname { Aim } ( X ); this is essentially a generalisation of the Kuratowski-WojdysB
   awski embedding of bounded metric spaces X into C ( X ), where we here consider arbitrary metric spaces ( bounded or unbounded ).