Absolute Retract

Let  be a class of topological spaces that is closed under homeomorphism, and let  be a topological space. If  and for every  such that ,  is a retract of , then  is an absolute retract for the class .

These notions can be generalized to category theory, and because there are category-theoretic versions, there are also other more specific versions, as in universal algebra and modern algebra.

REFERENCES:

Borsuk, K. Theory of Retracts. Warszawa, Poland: PWN, 1967.

Charatonik, J. J. and Prajs, J. R. "On Local Connectedness of Absolute Retracts." Pacific J. Math. 201, 83-88, 2001.

Hu, S. T. Theory of Retracts. Detroit, MI: Wayne State University Press, 1965.

Kuratowski, K. Topology, 2. New York: Academic Press, 1968.