Spaces of AANRs
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- by Zvonko Čerin PDF
- Proc. Amer. Math. Soc. 83 (1981), 609-615 Request permission
Abstract:
For a metric space $X$, let ${\text {AAN}}{{\text {R}}_{\text {C}}}(X)$ denote the hyperspace of all nonempty approximative absolute neighborhood retracts in the sense of Clapp in $X$ topologized with the metric of continuity. We show that ${\text {AAN}}{{\text {R}}_{\text {C}}}(X)$ is topologically complete iff $X$ is topologically complete. Some subsets of the first Baire category in ${\text {AAN}}{{\text {R}}_{\text {C}}}(X)$ for a $Q$-manifold $X$ are identified. For example, the collection ${\text {AAN}}{{\text {R}}_{\text {N}}}(X)$ of all nonempty approximative absolute neighborhood retracts in the sense of Noguchi in $X$ is such a subset.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 609-615
- MSC: Primary 54B20; Secondary 54C15, 54C55, 54E52
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627704-8
- MathSciNet review: 627704