Comment by MoltenMan

Most of this is very true, except for the one caveat I'll point out that a space complexity O(P(n)) for some function P implies at least a O(cubedroot(P(n))) time complexity, but many algorithms don't have high space complexity. If you have a constant space complexity this doesn't factor in to time complexity at all. Some examples would be exponentiation by squaring, miller-rabin primality testing, pollard-rho factorization, etc.

Of course if you include the log(n) bits required just to store n, then sure you can factor in the log of the cubed root of n in the time complexity, but that's just log(n) / 3, so the cubed root doesn't matter here either.