(Infinitely many topological types in dimension 4) Let $T^{3}$ denote a flat $3$-torus. According to Anderson [A93], there is a collapsing sequence of manifolds $(M^{4}_{j},d_{j})\stackrel{{\scriptstyle d_{GH}}}{{\longrightarrow}}T^{3}$ satisfying

		$\displaystyle{\rm diam}(M^{4}_{j})\leq 1\,,$
		$\displaystyle|{\rm Ric}_{M^{n}_{j}}|\leq\epsilon_{j}\to 0\,,$
		$\displaystyle{\rm Vol}(M^{4}_{j})\to 0\,,$
		$\displaystyle b_{2}(M^{4}_{j})\to\infty\,,$		(2.11)

where $b_{2}(M^{4}_{j})$ denotes the second Betti number of $M^{4}_{j}$. In particular, Theorem 1.4 , the finiteness theorem in dimension $4$, does not extend to the case in which the lower volume bound is dropped.