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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The space of retractions of a $ 2$-manifold


Author: Neal R. Wagner
Journal: Proc. Amer. Math. Soc. 34 (1972), 609-614
MSC: Primary 54C15
MathSciNet review: 0295282
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Abstract: Let $ {M^2}$ be a 2-manifold and let $ \Lambda $ be the embedding of $ {M^2}$ into its space of retractions which maps each point to the constant retraction to that point. Denote by $ \mathcal{L}({M^2})$ the component containing the image of $ \Lambda $. The embedding $ \Lambda $, with range restricted to $ \mathcal{L}({M^2})$, is shown to be a weak homotopy equivalence if $ {M^2}$ is compact, or if $ {M^2}$ is complete and the metric topology is used.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295282-6
Keywords: Retract, retraction, two-manifold, weak homotopy equivalence, function space, compact-open topology, sup-metric, selection, Riemann surface, conformal mapping, zero-regular convergence
Article copyright: © Copyright 1972 American Mathematical Society