M-embedded subspaces of certain product spaces

A subspace Y of a space X is said to be M-embedded in X if every continuous f : Y → Z with Z metrizable extends to a continuous function f ¯ : X → Z . pological spaces X i ( i ∈ I ) and J ⊆ I , set X J : = ∏ i ∈ J X i . thors prove a general theorem concerning κ-box topologies and pseudo- ( α , κ ) -compact spaces, of which the following is a corollary of the special case κ = α = ω . m X I and π J [ Y ] = X J for all ∅ ≠ J ∈ [ I ] < ω + , and if each X J , for ∅ ≠ J ∈ [ I ] < ω , is Lindelöf, then Y is M-embedded in X I . l results in Chapter 10 of the book [W.W. Comfort, S. Negrepontis, Chain Conditions in Topology, Cambridge Tracts in Math., vol. 79, Cambridge Univ. Press, 1982] depend on Lemma 10.1, of which the given proof was incomplete. A principal contribution here is to furnish a correct proof, allowing the present authors to verify and unify all the results from Chapter 10 whose status had become questionable, and to extend several of these.