Not sure what you mean by "memory requirement" and "theoretical time". If you don't access the memory, what do you mean by saying you "need" it? If a turing machine — or a computer program, for that matter — uses, i.e., "visits", exponentially many memory cells, then, indeed, its computing time cannot be polynomial. But note that every turing machine theoretically has infinite memory. The question is how much of it is actually used. PSPACE consists of those problems that can be solved by a turing machine that uses no more than p(n) memory, where p(n) is some polynomial in the input length n. Note that, for PSAPCE, time is unrestricted. So obviously P and NP are subsets of PSPACE, but it is unknown whether they are proper subsets.