A simply connected partition of a compact manifold

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1975

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Abstract

This paper investigates the problem of partitioning m-manifolds. In the second chapter starting with a positive number [epsilon], a compact, connected metric manifold is first covered by a finite collection of m-balls, each with diameter less than [epsilon]. Then an m-ball is put in each one and each one grows to end up with a partition which is simply connected in all dimensions. Piecewise linear mappings are used throughout.

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