# Comparing Topologies

/**coarser**than another topology $\tau_2$, and we write $\tau_1\subseteq\tau_2$, if every open set in $\tau_1$ is

*also*an open set in $\tau_2$. In this scenario, we also say $\tau_2$ is

**finer**than $\tau_1$. But other folks like to replace "coarser" by "smaller" and "finer" by "larger." Still others prefer to use "weaker" and "stronger." But how can we keep track of all of this? Personally, I like to think in terms of (and while sipping a cup of) coffee!