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)
- I don't recall seeing a link to a proof of that statement. Where is it justified? Abcxyz 10:11, 18 March 2012 (EDT)
Moved into Definition talk:Continuous Mapping (Topology)/Point. --prime mover (talk) 21:58, 3 November 2012 (UTC)
Too many things
Continuity at a point and continuity on a set are one pair of concepts.
Continuity by open sets is a way of talking about continuity everywhere, and should probably be a subdefinition of that.