continuous function

Also known as continuous map, continuous application, continuous transformation

function such that the preimage of an open set is open

AI overview

A continuous function is one where small changes in the input produce small changes in the output, with no sudden jumps or breaks. This concept matters because it allows mathematicians to study how functions behave smoothly and predictably, which is essential for understanding everything from physics to engineering to economics.

AI-generated from the Wikipedia summary — may contain errors.