On R∞ and Q∞-manifolds

AbstractWe give a characterization of manifolds modeled on R∞= dir lim or RnQ∞=dir lim Qn, where Q is the Hilbert cube, and elementary short proofs of the Open Embedding Theorem for these manifolds and the following theorem generalizing the Stability Theorem: Each fine homotopy equivalence between these manifolds is a near homeomorphism. Moreover we establish the Open Embedding Approximation Theorem