Polish topology

Polish topology refers to the study of topological spaces that are both separable (having a countable dense subset) and completely metrizable (their topology can be derived from a complete metric). These spaces are important in analysis and descriptive set theory because they provide a well-behaved setting for studying continuity, limits, and function spaces. Classic examples include real numbers with the standard topology, which are both separable and complete. Polish spaces serve as fundamental building blocks in many areas of mathematics, providing a framework for understanding complex structures through manageable, highly-structured spaces.