Fréchet spaces

A Fréchet space is a type of mathematical space used in advanced analysis, especially in the study of functions. It’s a complete, locally convex space equipped with a countable set of measurements called seminorms that define how close two elements are. These spaces are generalizations of Banach spaces, allowing for more flexibility while still maintaining a well-behaved structure that supports rigorous analysis. Essentially, they provide a framework to analyze functions and sequences where convergence and continuity can be understood using multiple, compatible ways of measuring size or distance.