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Let M be an F-manifold, that is, a separable, metric manifold modelled on an infinite-dimensional Fréchet space. The question was raised at a problem seminar this January (1969) at Cornell Univer­ sity whether homotopic embeddings of another F-manifold in M are isotopic. In this note the affirmative answer is given and a stronger result established. Given an open cover °\l of a space X, two maps ƒ and g of a space Y into X are said to be °\L-close provided that for each y in Y there is an element of % containing both f(y) and giy). The two maps are said to be pseudo-isotopic provided there is a map h: YXI-+X with %,0)=/(;y),

Approximating homotopies by isotopies in Fréchet manifolds