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We construct an example of an AR-map      f : X →  Y f:X \to Y      , where      X X       is a strongly countable dimensional compact AR and      Y Y       is a countable dimensional AR which is not strongly countable dimensional. Using this map we find a shrinkable decomposition of the pre-Hilbert space      l f 2 l_f^2       whose quotient map does not stabilize to a near homeomorphism. We also present a partial result concerning the question whether cell-like maps preserve countable dimensionality.

An AR-map whose range is more infinite-dimensional than its domain