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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple Question regarding C[0,1]

**Physics Forums | Science Articles, Homework Help, Discussion**