# Comparable topologies and transitivity

I am working on some homework for a topology class I am taking, and I was asked to compare a few topologies on a $$\mathbb{R}$$.

I won't go into detail about the topologies I worked with, but I was able to find that, for given topologies $$T_1, T_2, T_3,$$ on $$\mathbb{R}$$, $$T_2$$ is finer than $$T_1$$ and $$T_3$$ is finer than $$T_2$$, i.e. $$T_1 \subset T_2$$ and $$T_2 \subset T_3$$.

My question is, knowing this, can we say that $$T_3$$ is finer than $$T_1$$ by transitivity? I have to compare these two, and it would be much easier if I could say that, by transitivity, $$T_1 \subset T_3$$.