We construct a computable space bound $S(n)$, with $n2lessthanS(n)lessthann3$ and show by diagonalization that DSPACE [$S(n)$] = DSPACE [$S(n)$ log $n$]. Moreover, we can show that there exists an oracle $A$ such that DSPACE [$S(n)$] $\ne$ DSPACE[$S(n)$ log $n$]. This is a counterexample to the belief that is a theorem has contradictory relativizations, then is cannot be proved using standard techniques like diagonalization [7].