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I've read the proof of Urysohn's lemma from JAMES R. MUNKRES' text.I got it upto very extent.But,I'm not getting intuition for this proof.I liked the proof Proving that a compact subset of a Hausdorff space is closed by Brian M.Scott.I want someone to help me in getting the proof for Urysohn's lemma in the similar fashion.

Thank You!!

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    But the intuition part of that lemma is not that hard, I suppose: The idea is to construct a continuous functoin $\to[0,1]$ as a limit of finer and finer staircase functions. The ability needed to refine a staircase function is precisely the condition in the premise of the lemma. – Hagen von Eitzen May 01 '16 at 09:35
  • http://math.stackexchange.com/a/341019/4280 has an explanation by Brian as well. Does it help? – Henno Brandsma May 01 '16 at 12:19
  • http://math.stackexchange.com/q/1106917/4280 is also helpful. – Henno Brandsma May 01 '16 at 12:21

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