A continuous function is a Function
where the pre-image of every Open Set in is
Open in . A function in a single variable is said to be continuous at point if
where lim denotes a Limit. If is Differentiable at point , then it is also continuous at . If
and are continuous at , then
- 1. is defined, so that is in the Domain of .
exists for in the Domain of .
- 1. is continuous at .
- 2. is continuous at .
- 3. is continuous at .
- 4. is continuous at if
and is discontinuous at if .
- 5. is continuous at , where denotes , the Composition of the
functions and .
See also Critical Point, Differentiable, Limit, Neighborhood, Stationary Point
© 1996-9 Eric W. Weisstein