The space of intervals in a Euclidean space
Abstract
For a path-connected space X, a well-known theorem of Segal, May and Milgram asserts that the configuration space of finite points in Rn with labels in X is weakly homotopy equivalent to the n-th loop-suspension of X. In this paper, we introduce a space In(X) of intervals suitably topologized in Rn with labels in a space X and show that it is weakly homotopy equivalent to n-th loop-suspension of X without the assumption on path-connectivity.
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