Let me suggest and alternative proposal. (Partly also to make it possible for users to vote/comment also on this suggestion).
Suggestion. Let us keep only one dimension-theory tag. However, we should clearly indicate in the tag-info that:
- The tag includes the dimension as used in topology. (Such as Lebesgue covering dimension, small and large inductive dimension and similar notions. See also: Dimension theory on Wikipedia.)
- The tag includes dimension theory as used in commutative algebra. (Such as Krull dimension and some other notions of dimension used for rings and modules. See also: Dimension theory (algebra) on Wikipedia.)
- If needed, some other types of dimension should be mentioned explicitly. (For example, at the moment the tag-excerpt and the tag-wiki for (dimension-theory) explicitly mention Hausdorff dimension).
- This probably goes without saying, but the tag-info should also clearly state that this tag is not for dimension of vector spaces (as used in linear algebra).
One of the reasons for this proposal is that the discussion so far already suggests that it is unclear how many separate tags should arise from the existing dimension-theory. (The question suggested two, but it's possible that some users might prefer to split various types of dimensions related to fractals from topological notions of dimension. If we end up with three tags, the boundaries become fuzzy.)
For searching, one can still refine search with addition of some other tags, for example dimension-theory+general-topology, dimension-theory+fractals. dimension-theory+algebraic-geometry or dimension-theory+commutative-algebra, etc. (Although I have to admit that keeping this under single tag makes life a bit more difficult for people that are following that tag and are only interested in one of the meanings of dimension theory.)