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Decomposition spaces of En Hutchings, John Edward

Abstract

This paper is an introduction to the study of the problem: what decomposition spaces of Eⁿ are homeomorphic to Eⁿ? An introductory section on the elementary properties of decompositions and decomposition spaces is followed by characterizations of the decomposition spaces of E¹ and E² which are homeomorphic to E¹ and E² respectively. The characterization for E² follows Moore-Whyburn. We then give sufficient conditions for a decomposition space of Eⁿ to be Eⁿ, following Bing's recent work. No characterization is known for general Eⁿ . This paper reflects the status of the question as of, roughly, 1957. There has been essentially no progress since then.

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