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Are these two phrases saying the same thing?

An open set $\mathcal{N}$ containing the level set $\mathcal{L}$.

A neighborhood $\mathcal{N}$ of the level set $\mathcal{L}$.

bof
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M6126
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    Sometimes, "neighborhood of something" means "any set containing an open set containing that something". But most commonly, the interpretation is the one you gave. – Giuseppe Negro Sep 27 '18 at 09:39
  • Great, thank you! – M6126 Sep 27 '18 at 10:02
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    Is disagree with Giuseppe Negro's "most commonly" judgement. A neighborhood is normally not required to be open. If so, one usually says it is an open neigborhood. See https://math.stackexchange.com/q/157735 . But of course it depends on conventions. – Paul Frost Sep 27 '18 at 15:48

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