Abstract
Using the intrinsic definition of shape we prove an analogue of well known Borsuk’s theorem for compact metric spaces. Suppose X and Y are locally compact metric spaces with compact spaces of quasicomponents QX and QY. For a shape morphism f: X → Y there exists a unique continuous map f# :QX → QY, such that for a quasicomponent Q from X and W a clopen set containing f# (Q) the restriction f:Q → W, is a shape morphism, also.
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