I was watching a Physics TV show, When someone called Alex Filippenko said that when there was the Big Bang, the Space extended at a speed faster than speed of light. He said that it wasn't against the theory of relativity because space isn't a particle and can go faster than speed of light.
As far as I know it's true. Imagine space is like a stress ball squeezed down in your fist. When you open your hand, space expands at some rate. Now imagine that whilst it's doing so, you can tap it with a spoon and watch it wobble as waves run through it. The expansion rate could be faster than the propagation speed of the waves. Particularly if it's big.
So I wanted to know if that is a fact?
I think it's a fact. Quite apart from what you see on the Discovery Channel, I like to think I know a thing or two about relativity and cosmology. And I have to say: this checks out.
And otherwise how could the light go further if space around wasn't going at least as fast as light?
The early universe is sometimes likened to a black hole. Something called the "coordinate" speed of light is zero at the black hole event horizon, see Wikipedia. So you could claim that it was zero in the very early universe, which appears to have expanded somewhat. So when the universe first started expanding at the time of the Big Bang, it's possible it did so when the "coordinate" speed of light was zero. If so, it would have been expanding faster than light even then. And as far as we know, it still is.