# First Cech cohomology of manifolds

Let $X$ be a compact connected manifold (with or without boundary) and let $H_1(X)$ denote its first Cech integral cohomology group or, equivalently, its first cohomotopy group. Is it true that $H_1(X)$ is finitely generated even if $X$ is not triangulable? Could you please also provide a reference?

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