Abstract. Using the intrinsic definition of shape we prove an analogue of well known Borsuks 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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