Extending equivariant maps into spaces with convex structure |
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| Institution: | Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510, Mexico;The University of Florida, Gainsesville FL, USA;The University of Zagreb, Zagreb, Croatia;The University of Florida, Gainsesville FL, USA;The University of Zagreb, Zagreb, Croatia |
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| Abstract: | We prove that if G is a compact Lie group, Y a G-space equipped with a topological local convex structure compatible with the action of G, then Y is a G-ANE for metrizable G-spaces. If, in addition, Y has a G-fixed point and admits a global convex structure compatible with the action of G, then Y is a G-AE. This is applied to show that certain hyperspaces related to the Banach–Mazur compacta are equivariant absolute extensors. |
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