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A remainder of the Hilbert space l2 is a space homeomorphic to Z\l2, where Z is a metrizable compact extension of l2, with l2 dense in Z. We prove that for any remainder K of l2, every non-one-point closed image of K either contains a compact set with no transfinite dimension or contains compact sets of arbitrarily high inductive transfinite dimension ind. We shall also construct for each natural n a σ-compact metrizable n-dimensional space whose image under any non-constant closed map has dimension at least n, and analogous examples for the transfinite inductive dimension ind (this provides a rather strong negative solution of a problem in [EnP]).

On closed mappings of 𝜎-compact spaces and dimension