Products of decompositions of 𝐸ⁿ

Smith, Brian J.

doi:10.1090/S0002-9947-1973-0328946-1

Products of decompositions of $E^{n}$
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by Brian J. Smith PDF

Trans. Amer. Math. Soc. 184 (1973), 31-41 Request permission

Abstract:

In this paper we give a sufficient condition for the existence of a homeomorphism $h:{E^m}/G \times {E^n}/H \to {E^{m + n}}$, where G and H are u.s.c. decompositions of Euclidean space. This condition is then shown to hold for a wide class of examples in which the decomposition spaces ${E^m}/G$ and ${E^n}/H$ may fail to be Euclidean.

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