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The loop space $Ω_X$ of a pointed topological space $X$ is the space of based maps from the circle $\mathbb S^1$ to $X$ with the compact-open topology.

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Topological characterisation of loop spaces

Let $\Omega\colon \mathrm{Top}_*\to\mathrm{Top}_*$ be the loop space functor assigning to each pointed topological space $X$ the pointed space consisting of all based continuous maps $S^1\to X$ equipp …
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