The underlying set of the fundamental group of X is the set of based homotopy classes from the circle to X, denoted [S^1,X]. For general spaces X and Y, there is no natural group structure on [X,Y], but when there is a natural group structure, X is called a co-H-space.

See also

Co-H-Group, Fundamental Group, H-Space, Homotopy Class

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Cite this as:

Weisstein, Eric W. "Co-H-Space." From MathWorld--A Wolfram Web Resource.