2011/05/20 by Robert Alkins, Alkins, Robert, Vesko Valov +1
Mathematics · #54C20 #54C55 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #math.FA #math.GN #msc:54C20 #msc:54C55
paper · pdf · doi:10.48550/arxiv.1105.4122
19 pages
arxiv created 2011/05/20 · openalex publication_date 2011/05/20 · arxiv updated 2011/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the supports of a class of real-valued maps on C*(X) introduced by Radul. Using this description, a characterization of compact-valued retracts of a given space in terms of functional extenders is obtained. For example, if X⊂ Y, then there exists a continuous compact-valued retraction from Y onto X if and only if there exists a normed weakly additive extender u\colon C*(X)→ C*(Y) with compact supports preserving min (resp., max) and weakly preserving max (resp., min). Similar characterizations are obtained for upper (resp., lower) semi-continuous compact-valued retractions. These results provide characterizations of (not necessarily compact) absolute extensors for zero-dimensional spaces, as well as absolute extensors for one-dimensional spaces, involving non-linear functional extenders.