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Authors: Yu-Lin Chou
That every Euclidean subset homeomorphic to the ambient Euclidean space is open, a version of invariance of domain, is a relatively deep result whose typical proof is far from elementary. When it comes to the real line, the version of invariance of domain admits a simple proof that depends precisely on some elementary results of ``common sense''. It seems a pity that an elementary proof of the version of invariance of domain for the real line is not well-documented in the related literature even as an exercise, and it certainly deserves a space. Apart from the main purpose, as we develop the ideas we also make present some pedagogically enlightening remarks, which may or may not be well-documented.
Comments: 3 Pages. expository article
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[v1] 2020-11-06 09:04:24
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