In topology, several separation axioms (such as Hausdorff, completely regular, normal, ...) and countability axioms (such as first countability or separability) are often used ant there are also some questions about them on this site. Hence it is not entirely surprising that we also have tags separation-axioms and countability-axioms for such questions. And also tag-info for both separation axioms and countability axioms have been created. Both these tags have been around for some time, the tag for separation axioms was created in September 2013, the tag for countability axioms was created in February 2016.
However, I think that creating separate tags for each one of them might lead to having too many tags. (Just consider the fact, that many questions might be about implication between two separation properties, so such question would quite naturally be tagged with both.) This is perhaps less clear for countability axioms, but there are certainly many separation axioms.
This questions was prompted by the fact that the tag separable-spaces has been created not so long ago. (Apart from this one, I do not know about a tag for single one of these properties.) However, since these properties are similar, perhaps it makes more sense to discuss them all at once rather than each of them separately.
- Should we have separate tags for some of separation axioms? Should we have separate tags for some of countability axioms? (If yes, for which ones and what would be reasonable names for those tags be?)
- Are there some properties which should be added to the tag-info, so that it is clearer which topological properties are covered by these two tags.
- Should we create synonyms such as1 hausdorff-spaces $\to$ separation-axioms, so that this helps users who are looking for tag when asking about Hausdorff spaces (and similarly for other properties)? Or does it suffice to create synonyms only in cases when some user creates such tag?
1Perhaps a better name would be hausdorff-property or hausdorff-axiom for the reasons explained in quid's post. However, this was merely given here as an example - as we are already discussing these tags, we might discuss such possible "redirects" at the same time. (Both whether they might be useful and if yes, what could a good choice of name be.)
EDIT: Since there was no activity on this post for some time, I have accepted the most upvoted answer. As a result of this discussion, I have created first-countable and second-countable tags. (Both of them are still small enough, if we want to change the tag names.)
I will start retagging the questions tagged countability-axioms in a reasonable pace until we eventually remove the tag. List of the questions which had this tag before the retagging started can be found here.