Abstract
This paper is largely devoted to proving the following result: Let E be a Fréchet space homeomorphic to its own countable infinite product, M be a paracompact manifold modeled on E, and let K ⊂ M be closed. Then there exists a homeomorphism of M onto M × E taking K into M × {0 } iff for each non-null, homotopically trivial open set U in M, U⧹ K is non-null and homotopically trivial. A similar result for E = ▪ 2 (separable Hilbert space) is known.
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