I am trying to show that there exists a topology in which $ s(X) \le d(X) $. I am working with the co-countable topology with an infinite topological space X. I understand the $d(X)$ is uncountable and the $ s(X) $ is countable.
For the density, I understand that I have to show that no countable set is dense.
For the spread, I know a little less. I know that I have to take an uncountable subset of X and show the spread is countable in the co-countable topology.
I understand these concepts however I am having trouble writing them on paper.
Any hints and direction would be appreciated!