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Metrization of the coarse shape groups

By using certain ultrametrics on special sets of pro and pro*-morphisms, we topologize shape and coarse shape groups when they refer to compact metric spaces and we get topological groups. In such a manner we obtain a new invariant on algebraic and on topological level, as well, which can be useful tool in distinguishing homotopy and (coarse) shape type of topological spaces.

Metrization, coarse shape groups

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