Let be a subset of . A function is continuous at a point when given there is a neighbourhood of such that for every . When the same neighbourhood can be chosen for all functions , the family is said to be equicontinuous. More precisely:
Definition - Let be a subset of . The set of functions is said to be equicontinuous at if for every there is a neighbourhood of such that for every and every we have
The set is said to be equicontinuous if it is equicontinuous at every point .
If a subset is totally bounded under the uniform metric, then is equicontinuous.
- 1 J. Munkres, Topology (2nd edition), Prentice Hall, 1999.
|Date of creation||2013-03-22 18:38:10|
|Last modified on||2013-03-22 18:38:10|
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