Abstract
The aim of this paper is to study topological features of Sub 4 X ; the finite subset space of cardinality at most four associated to a topological space X. We determine its connectivity in terms of the connectivity of X, hence answering a conjecture of Christopher Tuffley in that case. We compute the Euler characteristic of Sub 4 X for any topological space X. We provide complete homology computations and determine the rational homotopy type of Sub 4 S d for any d-dimensional sphere.
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