Brouwer degree

The Brouwer degree is a mathematical concept that measures how many times a continuous function maps one space onto another, considering orientation. For example, if you think of a function as a way of wrapping or covering a surface, the degree tells you whether the wrapping is done once, multiple times, or in reverse. It's a tool used in topology to understand how spaces relate under continuous transformations, providing a sort of "count" that remains constant under deformation, and is useful for determining whether solutions exist to certain equations or how complex a mapping is.