Information AboutEquicontinuous |
| CATEGORIES ABOUT EQUICONTINUITY | |
| continuous mappings | |
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If a sequence of continuous functions Converges Pointwise , then the limit is not necessarily continuous (a Counterexample is given by the family defined by ''f''''n''(''x'') = arctan ''nx'', which converges to the discontinuous Sign Function ). However, if the sequence is equicontinuous, then we can conclude that the limit is continuous. DEFINITIONS Let {''f''''n''} be a sequence of functions from ''X'' ⊂ R to R (more general functions are considered below). |
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