Eilenberg-Mac Lane Space

For any Abelian Group and any Natural Number , there is a unique Space (up to Homotopy type)such that all Homotopy Groups except for the th are trivial (including the 0th HomotopyGroups, meaning the Space is path-connected), and the th Homotopy Group isIsomorphic to the Group . In the case where , the Group can benon-Abelian as well.

Eilenberg-Mac Lane spaces have many important applications. One of them is that every Topological Space has theHomotopy type of an iterated Fibration of Eilenberg-Mac Lane spaces (called a Postnikov System). Inaddition, there is a spectral sequence relating the Cohomology of Eilenberg-Mac Lane spaces to the HomotopyGroups of Spheres.

• Factor Space
• Fagnano's Point
• Fagnano's Problem
• Fagnano's Theorem
• Fair Game
• Fairy Chess
• Fallacy
• False
• False Position Method
• Faltung (Form)
• Faltung (Function)
• Fan
• Fano Plane
• Fano's Axiom
• Farey Sequence
• Farey Series
• Farkas's Lemma
• Faro Shuffle
• Far Out
• Far-Out Point
• Fast Fibonacci Transform
• Fast Fourier Transform
• Fat Fractal
• Fatou Dust
• Fatou Set