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  Functions between metric spaces [ edit ] Euler diagram  of types of functions between metric spaces. Unlike in the case of topological spaces or algebraic structures such as  groups  or  rings , there is no single "right" type of  structure-preserving function  between metric spaces. Instead, one works with different types of functions depending on one's goals. Throughout this section, suppose that  ( � 1 , � 1 )  and  ( � 2 , � 2 )  are two metric spaces. The words "function" and "map" are used interchangeably. Isometries [ edit ] Main article:  Isometry One interpretation of a "structure-preserving" map is one that fully preserves the distance function: A function  � : � 1 → � 2  is  distance-preserving [12]  if for every pair of points  x  and  y  in  M 1 , � 2 ( � ( � ) , � ( � ) ) = � 1 ( � , � ) . It follows from the metric space axioms that a distance-preserving function is ...

  Limit of a sequence 40 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia For the general mathematical concept, see  Limit (mathematics) . This article  needs additional citations for  verification .  Please help  improve this article  by  adding citations to reliable sources . Unsourced material may be challenged and removed. Find sources:   "Limit of a sequence"  –  news   ·   newspapers   ·   books   ·   scholar   ·   JSTOR   ( May 2017 )  ( Learn how and when to remove this template message ) The sequence given by the perimeters of regular  n -sided  polygons  that circumscribe the  unit circle  has a limit equal to the perimeter of the circle, i.e.  2 � � . The corresponding sequence for inscribed polygons has the same limit. n n  sin(1/ n ) 1 0.841471 2 0.958851 ... 10 0.998334 ... 100 0.999983 As the positiv...