Fréchet Space

A Fréchet space is a type of mathematical structure used in advanced analysis, characterized by being a complete space with a metric that allows for measuring how close functions or elements are, and is built using many ways of measuring (called seminorms). Unlike more familiar spaces, it doesn’t require all sequences to converge based on a single measurement but instead uses a compatible system of measurements to ensure limits are well-defined. This makes Fréchet spaces flexible for studying complex functions and infinite-dimensional problems, especially when analyzing smooth or rapidly changing behaviors in various mathematical contexts.