Abstract
Let G be a compact metrizable group and H its closed subgroup. We prove that every compact metrizable G-space over G/H admits a G-fibrant extension over G/H. This implies that the functor of twisted product G×H− takes H-fibrant extensions to G-fibrant extensions. In particular, the twisted product G×HS is a G-fibrant space when S is a compact H-fibrant space.
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