We compare Schröder’s approach to computable topology with that of Weihrauch and Grubba. To do this, we introduce different notions of “effectively second countable” represented spaces, and prove that the most restrictive of these is precisely what was considered by Weihrauch and Grubba under the name “computable topological space”. We then show that this strong notion of effective second countability is necessary in Schröder’s Effective Metrization Theorem, but that some classical statements can be effectivized thanks to weaker hypotheses, we give as an example the statement “A second countable space is separable”.