2:36 AM
I was a bit unsure about tagging this question.
2

Is there a topology induced in $\mathcal P (X)$ for an infinite set $X$? Intuitively, if $s_1 \supseteq s_2 \supseteq s_3 ...$ and $\bigcap_i s_i = s$ then we could say $s$ is the limit of $\{s_i\}$. But I don't exactly know how to define the open sets to make that formal. Even better: Is there...

However, I have decided to add and . My reasoning was approximately like this:
There is a notion of $\limsup X_n$ and $\liminf X_n$ of sets. And if we follow the tag-wiki questions about them we should use .
We can also say that $\lim X_n=X$ if $\limsup X_n=\liminf X_n=X$.
If I am not mistaken, the convergence of decreasing system of sets described in the question is special cases of this. So I guess it should be tagged the same.
The tag-info for limsup-and-liminf says: "For questions concerning the limsup/inf of sets, please add the tag. For questions involving abstract partial orders, use also the tag."

1 hour later…
3:43 AM
@AsafKaragila Did you have time to think about your suggestion for ? Or is it better to keep and separately? Should we bring this up on meta?
Or perhaps will we wait for 2017 tag management thread? Coming soon to your meta.

4:01 AM
I have added and here. Do they fit? Any other suggestions?
13

$$\frac{n}{\infty} + \frac{n}{\infty} +\dots = \frac{\infty}{\infty}$$ You can always break up infinity/infinity into the left hand side, where n is an arbitrary number. However, on the left hand side $\frac{n}{\infty}$ is always equal to 0. Thus $\frac{\infty}{\infty}$ should always equal $0$.

8 hours later…
11:44 AM
@MartinSleziak This post was deleted by the OP (=arjafi).
Shortly before deletion I received ping from him, the text of the comment was: "I'll come back to this when there is an actual need."
That seems like a reasonable decision.
in Math Mods' Office, yesterday, by Martin Sleziak
It's probably moot point at the moment anyway. We will see whether somebody tries to create the tag again.
in Math Mods' Office, yesterday, by Martin Sleziak
And if it is created, whether it survives longer than a few hours.

12 hours later…
11:22 PM
It's not really my field or my fields, but is product-space a useful tag? Mostly it seems like topology with a couple other questions there. I think to have a tag for topology on product spaces can be useful, but to mix all kinds of product spaces, seems a bit like "subspaces." — quid 2 hours ago
@quid I do my best to help following the existing tag-excerpt and using this tag only in context of topology and measure theory. If we decide to have separate tag only for topological products, it should probably be discussed in separate post. — Martin Sleziak 30 mins ago
The (product-space) tag was around in this form for some time, the tag excerpt was created in 2013. I did not find any discussion on meta mentioning this tag before 2015: What should be in (products) tag?. Around the same time it was also mentioned in chat, see here and here. — Martin Sleziak 30 mins ago
"following the existing tag-excerpt and using this tag only in context of topology and measure theory" (my emphasis) While likely a good idea, that's not what the description says. It says "the structure of product space, in the context of topology or measure theory for example." (my emphasis) — quid 20 mins ago
I agree with your last comment. And certainly questions about product metric or product of normed spaces fall under the tag description. Having this tag is probably not ideal, but it is certainly better than having in the same tag, for example, matrix product, categorical product, product of numbers. Whether it would be useful to divide (product-spaces) into smaller tags, I am not entirely sure. BTW if a longer discussion about this is needed, we can take it to chat. — Martin Sleziak 1 min ago