Question

Just making sure I'm understanding the concept of "coarser" and "finer" topologies: Would it be correct to say that given a set X, the "finest" topology possible would be the discrete topology (all possible subsets of X), and the "coarsest" topology possible would be the trivial topology (just the null set and all of X)?

Answer 1

That's the correct way to think about it.

Answer 2

Great, thank you!

Answer 3

You're welcome.