D. W. Henderson established the metric topology vertion of J. H. C. Whitehead's Theorem on small subdivisions of simplicial complexes. However, his proof is valid only for locally finite-dimensional simplicial complexes. In this note, we give a complete proof of Henderson's Theorem for arbitrary simplicial complexes.
"Small subdivisions of simplicial complexes with the metric topology." J. Math. Soc. Japan 63 (3) 789 - 800, July, 2011. https://doi.org/10.2969/jmsj/06330789