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.
This entry contributed by Matt Insall (author's link)
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.
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