A topological space is said to be an H-space (or Hopf-space) if there exists a continuous binary operation and a point such that the functions defined by and are both homotopic to the identity map via homotopies that leave fixed. The element is sometimes referred to as an ‘identity’, although it need not be an identity element in the usual sense. Note that the definition implies that .
Topological groups are examples of H-spaces.
If is an H-space with ‘identity’ , then the fundamental group is abelian. (However, it is possible for the fundamental group to be non-abelian for other choices of basepoint, if is not path-connected.)
|Date of creation||2013-03-22 16:18:18|
|Last modified on||2013-03-22 16:18:18|
|Last modified by||yark (2760)|