Topology of Infinite-Dimensional Manifolds

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The book explores infinite-dimensional manifolds, focusing on various model spaces such as Hilbert spaces, the Hilbert cube, and dense subspaces of Hilbert spaces. It examines their roles as universal spaces for absolute Borel spaces, along with the direct limits of Euclidean spaces and Hilbert cubes. The text delves into the intricate relationships and properties of these spaces, particularly highlighting the homeomorphism to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology.