Vol. 47, No. 1, 1973

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On the countable union of cellular decompositions of n-manifolds

William L. Voxman

Vol. 47 (1973), No. 1, 277–285

Suppose that G1,G2 are cellular upper semicontinuous decompositions of an n-manifold with boundary M(n4) such that for i = 1,2,,M∕Gi is homeomorphic to M. Let G be the decomposition of M obtained from the decomposition of Gi in the following manner. A set g belongs to G if and only if g is a nondegenerate element of some Gi or g is a point in M (i=1HGi). It will be shown that if the various decompositions fit together in a “continuous” manner and if G is an upper semicontinuous decomposition of M, then M∕G is homeomorphic to M.

Mathematical Subject Classification
Primary: 57A60
Received: 6 March 1972
Published: 1 July 1973
William L. Voxman