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Absolute Retract


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

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)

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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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Absolute Retract

Cite this as:

Insall, Matt. "Absolute Retract." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AbsoluteRetract.html

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