Question 8

Question

What is a continuous function?

Answer

A continuous function is a function that has does not abruptly change in value.

We say that $f$ is continuous (at every $x$) if $f^{-1}(A)\equiv \{x\in X|f(x)\in A\}$ is open for every open $A\subset Y$.

Example of a Non-Continuous

$f(x)=\frac{1}{x}$ is not a continuous function as at $x=0$ there is an abrupt change in value, and the value there is undefined.