The class of decision problems solvable in space O(f(n)) by a reversible Turing machine (a deterministic Turing machine for which every configuration has at most one immediate predecessor).
Was shown to equal DSPACE(f(n)) [LMT97].
Same as NPSPACE, but with f(n)-space (for some constructible function f) rather than polynomial-space machines.
Contained in DSPACE(f(n)2) [Sav70], and indeed RevSPACE(f(n)2) 95|[CP95].
NSPACE(nk) is strictly contained in NSPACE(nk+ε) for ε>0 [Iba72] (actually the hierarchy theorem is stronger than this, but pretty technical to state).