Consider three closed linear subspaces $C_1, C_2,$ and $C_3$ of a Hilbert space $H$ and the orthogonal projections $P_1, P_2$ and $P_3$ to them. Halperin showed that a point in $C_1\cap C_2 \cap C_3$ can be found by iteratively projecting any point $x_0 \in H$ onto all the sets in a periodic fashion. The limit point is then the projection of $x_0$ onto $C_1\cap C_2 \cap C_3$. Nevertheless, a non-periodic projection order may lead to a non-convergent projection series, as shown by Kopeck\'{a}, M\"{u}ller, and Paszkiewicz. This raises the question how many projection orders in $\{1,2,3\}^\mathbb{N}$ are ``well behaved'' in the sense that they lead to a convergent projection series. De Brito, Melo, and da Cruz Neto showed that the ``well behaved'' projection orders form a large subset in the sense of measure, as they have full product measure. We show that also from a topological viewpoint the set of ``well behaved'' projection orders is a large subset$:$ it contains a co-$\sigma$-porous subset with respect to a metric inducing the product topology.