Countable approximation of topological G-manifolds: Compact Lie groups G

Abstract Let G be a compact Lie group. (Compact) topological G -manifolds have the G -homotopy type of (finite-dimensional) countable G -CW complexes (2.5) . This partly generalizes Elfving's theorem for locally linear G -manifolds [14] , wherein the Lie group G is linear (such as compact).