Countable decompositions of Eⁿ

David G. Wright

Vol. 103 (1982), No. 2, 603–609

DOI: 10.2140/pjm.1982.103.603

Abstract

We investigate the nature of upper semicontinuous decompositions of Eⁿ that contain only countably many cellular nondegenerate elements. Such decompositions do not in general yield decomposition spaces which are homeomorphic to Eⁿ. However, we consider certain additional restrictions on the decomposition which insure that the decomposition space is homeomorphic with Eⁿ (n ≧ 5). It is interesting to note that these same restrictions do not guarantee that such a decomposition of E³ yields a decomposition space homeomorphic with E³.

Mathematical Subject Classification 2000

Primary: 57N15

Secondary: 54B15

Milestones

Received: 14 March 1980

Revised: 21 July 1981

Published: 1 December 1982