Eilenberg–Mac Lane spaces

Eilenberg–Mac Lane spaces are special mathematical objects used in algebraic topology to connect algebra and topology. They are characterized by having exactly one non-trivial type of “hole” or “loop” in a specific dimension. For example, an \( K(G, n) \) space has its n-dimensional features corresponding to a group \( G \). These spaces help mathematicians understand and classify more complex shapes by translating topological problems into algebraic ones, making them fundamental tools for studying the structure of spaces and how they can be mapped or transformed.