The Euler Characteristic of Finite Subset Spaces

2026/07/20 by Walid Taamallah
Mathematics · #math.AT

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Abstract

For a topological space X, the space of finite subsets Sub_n X consists of non-empty subsets of X of cardinality at most n. We compute the Euler characteristic of Sub_n X for any space X having the homotopy type of a finite CW complex. We obtain the explicit formula χ(Sub_n X) = ∑_i=1ⁿ \binomχ(X)i.

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