So if D={f is an element of C[0,1];f(1) does not equal 1}(adsbygoogle = window.adsbygoogle || []).push({});

and C[0,1] is the set of complex valued continuous functions on the interval [0,1], is there a function f such that f approaches 1 and f(1) does not equal 1?

I feel like there has to be one but I am unable to construct one since if the lim as x approaches 1 does not equal f(1)=1, then f wouldn't be continuous right?

I'm trying to show that D doesn't contain all of its limit points since that would be all that is required to show D is not closed.

Help with finding this function if there is one please.

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# Simple Question regarding C[0,1]

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