# Are there any complexity classes that can be solved in Polynomial Time that are not in PSPACE?

These would be problems solvable in Polynomial time with and only with pseudo-polynomial or Exponential Space. Do such problems exist? if so which complexity class are they? If not can you prove that every problem solvable in polynomial time is also solvable in polynomial space?

The space complexity is always bounded by the time complexity, since you cannot access more than $$t(n)$$ cells if you run for $$t(n)$$ time.
No. The amount of space used is upper-bounded by the running time. Each step of the Turing machine can only move one place on the tape. Therefore, $$P \subseteq PSPACE$$.