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In this question there is confusion about the answer because it appears (to me, anyway) that the origin was supposed to be rendered as not on or inside a simple closed curve; but the question is being answered as if the origin were merely not on the curve. This causes the problem to be ill-posed. How should the origin have been rendered precisely as not inside or on the curve?

Oscar Lanzi
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With the notation set up in that problem, I don't know of a way in notation alone.

In words, it's easy enough to say let $\gamma :[a,b]\to\Bbb{C}$ be a simple closed curve with $0$ not on $\gamma$ or in its interior.

Note

As pointed out by Ted Shifrin in the comments, in my original answer, I answered your question, which assumes that the curve is simple closed, but the linked question only assumes closed, and I ended up writing merely closed in my answer originally. That the curve is simple closed is important for the existence of the interior.

jgon
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    If it's not a simple closed curve, interior and exterior may not make sense. We need to talk about winding numbers, even if $\gamma$ is a $C^1$ mapping. – Ted Shifrin May 25 '19 at 23:52
  • @TedShifrin The OP here was assuming that the curve was a simple closed curve, but of course you're right, I should have been more careful in stating my answer. – jgon May 26 '19 at 00:02
  • Well, the original question said nothing about its being a simple closed curve. Or, if it did, I totally missed it. – Ted Shifrin May 26 '19 at 00:06
  • @TedShifrin Yes, the linked question said closed curve, but on this question the OP wrote simple closed curve, which is why I originally got confused likely. – jgon May 26 '19 at 00:07
  • The original question did say "closed curve" yet may well have meant "simple closed curve". This, too, is a nomenclature issue. – Oscar Lanzi May 26 '19 at 01:59
  • @OscarLanzi Indeed, it may well have meant that, the poster of the linked question seemed very confused about what the question was asking for, and it was missing sufficient context to disambiguate, so it's hard to say. – jgon May 26 '19 at 02:02