Electronic Version 18 (1993), 7-17

Robert N. Andersen, M. M. Marjonovic and Richard M. Scori

An interesting construction in topology is the nth symmetric product of a metric space X, denoted X(n), which is defined to be the hyperspace of n (n >= 1) or fewer points of X, metrized with the Hausdorff metric. An attraction of these spaces is that S¹(2) is homeomorphic to the Mobius Band and S¹(3) is homeomorphic to S³. In this paper we will see that the Dunce Hat also comes up in a natural way and this leads to a symmetric product definition of what we call ``higher dimensional Dunce Hats''.

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volume 18: table of contents
topology proceedings Electronic Version