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Francesco Polizzi
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I know that it holds even if $X$ has infinite dimension, but I am looking for thea specific argumentation forargument in the finite-dimensional case.

I know that it holds even if $X$ has infinite dimension, but I am looking for the specific argumentation for the finite-dimensional case.

I know that it holds even if $X$ has infinite dimension, but I am looking for a specific argument in the finite-dimensional case.

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How do I show that any finite-dimensional (absolute) CW-complex $X$ is locally contractible?

I know that it holds even if $X$ has infinite dimension, but I am looking for the specific argumentation for the finite-dimensional case.