G-fibrant extensions and twisted products.

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 × H S is a G -fibrant space when S is a compact H -fibrant space. [ABSTRACT FROM AUTHOR]