Continuous Maps

A continuous map is a function between two spaces where small changes in the input lead to small changes in the output. Think of it like drawing a smooth curve: if you make a tiny tweak to the starting point, the resulting point on the curve only shifts slightly. There are no abrupt jumps or breaks. This concept ensures the behavior of the function is predictable and smooth, making it essential in fields like calculus and topology for understanding how shapes and spaces relate without sudden disruptions.