# How should questions about Cantor space and Cantor cubes be tagged?

There exists a tag called . Based on the current revision of the tag-info it is about Cantor ternary set and also about generalization to fat Cantor set. Both of them have very similar constructions and are subsets of $[0,1]$.

It is well known that, as a topological space, the Cantor set is homeomorphic to the Cantor space $\{0,1\}^{\mathbb N}$ or $\{0,1\}^\omega$, i.e., countable power of 2-point discrete space. And this space can be generalized to Cantor cube $\{0,1\}^A$, where $A$ can be set of arbitrary cardinality.

IIRC I have seen a few questions about the Cantor space with (cantor-set) tag. (Of course, in some cases a question can be about both the Cantor set and Cantor space. For example, questions asking about proof that they are homeomorphic. So sometimes there is no clear division line between questions about the Cantor set and questions about the Cantor space.) I don't recall whether I have seen a questions about Cantor cubes tagged like this.

So the questions are:

• Should we have some tag for Cantor cubes (including the Cantor space). (In a sense tag can be considered as a kind of precedence, since it is a tag about the space $\omega^\omega$, which is similar to $2^\omega$. Some discussion about this tag can be found here.)
• If the answer to the preceding question is yes, then the other question arises: Should Cantor cubes be in the same tag sa Cantor set, or should these be two separate tags. (If the decision is that they belong into the same tag, then we should probably clarify this in the tag-info. And synonyms $\to$ and $\to$ would probably help correct tagging.)

And it is probably also worth mentioning that there was a suggestion to remove (cantor-set) tag completely, but results of the voting on this post did not show much support of that proposal. (However, there were not too many users who voted on that, at the moment the score is 1 with two upvotes and one downvote.)

• Using cantor-set seems fine. It signals what the basic object is, or at least what sort of object one is to find discussed in the question. If needed, the tag can be edited to include variants so it does not appear to be exclusively about the standard ternary set. Oct 28 '16 at 14:50
• I have edited the tag cantor-set in that fashion. Nov 2 '16 at 18:42

• What about a question not just involving a Cantor cube, but strictly about a Cantor cube, such as Is $2^{\frak{c}}$ separable? or What does $\text{cl}(\text{im}(e_\mathbb{N}))\subseteq 2^{2^{\mathbb{N}}}$ look like?. Sure they are in general-topology, but this tag is also one of the 10 largest tags on the site, so it doesn't really help in later finding such questions. Oct 28 '16 at 12:40