Generalized cohomology theory

Summary

A generalized (or extraordinary) cohomology theory is a contravariant functor from pairs of spaces to graded abelian groups. It satisfies all the Eilenberg–Steenrod axioms except the dimension axiom. So the cohomology of a point may be nonzero in many degrees. Topological K-theory, complex cobordism and stable cohomotopy are the main examples, and each such theory is represented by a spectrum.