Polish Space

A Polish space is a mathematical concept describing a type of space that is both complete and separable. "Complete" means every sequence of points that should converge does so within the space, and "separable" means it contains a countable, dense subset—think of a space that can be approximated well by just a countable set of points. These spaces are fundamental in analysis and topology because they provide a well-behaved environment for studying functions, limits, and structures, making them essential in many areas of mathematics and its applications.