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

- 1. is defined, so that is in the Domain of .
- 2. exists for in the Domain of .
- 3. ,

- 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 .

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1999-05-26