Definition talk:Continuous Mapping (Topology)

The current version states that: "The general definition for continuous mapping follows from the definition of continuity at a point for all points in the topology". However, this assertion is not justified. How about having two definitions for a continuous (everywhere) mapping: (1) the definition of continuous mapping in the current version, and (2) a mapping that is continuous at every point of its domain, according to the definition of continuity at a point? (We would then show that the two are equivalent.) Comments? Abcxyz 22:51, 17 March 2012 (EDT)


 * "However, this assertion is not justified." In what way is it not justified? --prime mover 02:01, 18 March 2012 (EDT)