Continuous Gas Leak Detection Camera

As you have it written now, you still have to show xâˆ'âˆ'âˆš x is continuous on [0, a) [0, a), but you are on the right track. As @user40615 alludes to above, showing the function is continuous at each point in the â€¦ I know that the image of a continuous function is bounded, but i'm having trouble when it comes to prove this for vectorial functions.

In general, is a bounded linear operator necessarily continuous (i guess the answer is no, but what would be a counter example?) are things in banach spaces always continuous? The continuous extension of f(x) f (x) at x = c x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on continuous extension throughout the web.