M-embedded subspaces of certain, product spaces

摘要

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. For topological spaces X_i (i ∈ I) and J is contained in I, set X_J := ∏_(i ∈ J) X)i. The authors 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.