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I would like to read a self-contained proof of the theorem of Rado that states that any second countable topological surface admits a triangulation. Actually, I would be content with the compact case.

References that are freely available online would be great. Book references are welcome too!

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up vote 4 down vote accepted

This is proved in a paper by Carsten Thomassen, The Jordan-Schonflies Theorem and the Classification of Surfaces, using graph-theoretic techniques.

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