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The homotopy classes of continuous maps between some non-metrizable manifolds

Mathieu Baillif
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Abstract

Let R be Alexandroff's long ray. We prove that the homotopy classes of continuous maps R^n \to R are in bijection with the antichains of P({1,...,n}). The proof uses partition properties of continuous maps R^n \to R. We also provide a description of $[X,R]$ for some other non-metrizable manifolds X.

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Mathieu Baillif. 2004-03-29. The homotopy classes of continuous maps between some non-metrizable manifolds. https://arxiv.org/abs/math/0403495

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