10:07 AM
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Quite often we have situation that discussion about a specific tag results in consensus that the tag should be removed. And the removal process means that the questions having that tag are retagged and thus bumped. In som cases, this might be quite a big number of questions. (For example, when th...

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In the metric space $(Z,d)$, let $A(z_0,\varepsilon)$ denote the closed ball$\left\lbrace z\mid d(z,z_0)\leq\varepsilon\right\rbrace$. Now let $X$ be an arbitrary space, let $Y$ a metric space and let $f:X \times Y \rightarrow Z$ be continuous in each variable separately. Let $\varepsilon>0$ and ...

I guess this might possibly be a useful tag - just look at posts about hemicontinuity or semicontinuity.
But maybe it would be better to have single tag for both upper and lower semicontinuity.
@AlexRavsky I see that you have created a new (upper-semicontinuity) tag. I wonder whether it would be better to have a single tag for both upper and lower semicontinuity. (Two separate tags for each of them seem to me a bit too specific.) I have mentioned this also in tagging chat room - we will see whether there will be some feedback on this there. — Martin Sleziak 13 secs ago

10:42 AM
@MartinSleziak @ Thanks for you attention.

1. Tags for upper and lower semicontinous maps are needed to concentrate attention of these sufficiently known notions, and I think this topic is sufficiently specific and far from ‘continuity’ tag.
2. I chose to create a separate tag for upper semicontinuity’, because sometimes upper and lower cases may need different approaches (for instance, for the maps to a space $\operatorname{exp} X$ endowed with “partial” Vietoris topology) or a question may be relevant to only one of th

@AlexRavsky Thanks for the response. Since we clearly disagree whether it's better to have one tag or two separate tags, I hope it's ok with you if I bring this up on meta.
We will see what other community members think about it. And based on the feedback there it can be decided what to do with the tag(s) for this topic.
Re: if needed, both upper and lower semicontinuity tag. The problem with this (or, more generally, with too specific tags) is that there are at most 5 spaces for tags allowed.
BTW it seems that many such questions have been tagged with continuity. So if the consensus if that the new tag should stay, some of older posts will need retagging.

1 hour later…
12:03 PM
@MartinSleziak OK.

@AlexRavsky Posted on meta:
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The tag upper-semicontinuity was created recently, here you can see a short discussion between me and the tag-creator. From this discussion it seems that the tag is intended both for functions and multifunctions. And also that the tag-creator would prefer to have separate tags for lower and upper...

I hope I did not misrepresent your position. And, of course, feel free to join the discussion in the comments under that post.

12:30 PM
I'm not sure that I see the value of a tag for semicontinuity. I'd be happy to hear more arguments pro/con on meta. — Asaf Karagila 22 mins ago
@AsafKaragila There is now a post on meta, so we can discuss this in more detail there. — Martin Sleziak 11 secs ago

3 hours later…
3:03 PM
The tag was created.
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In the book of General Topology by Munkres, at page 100, it is asked to prove that Every simply ordered set is a Hausdorff space in the order topology.The product of two Hausdorff space is again a Hausdorff space. Proof of the first statement: Let X be a topological space with the ord...

This tag was discussed before, maybe I should reread the discussion we had back then:
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On the last question: no there should be no synonym from hausdorff-spaces to separation-axioms. The issue is that somebody asking about a problem that happens to be placed in the context of a Hausdorff space might well use the former tag, while the question is not at all about separation axiom...

Anyway the most upvoted answer there says:
> I take exactly the opposite view of separation axioms: the single tag is the way to go. I’m perfectly happy to let it cover questions about the $T_1$ property, the Hausdorff property, normality, the Tikhonov property, etc. I see no benefit to having a separate tag for Hausdorff spaces, for instance: if the Hausdorff property is actually usefully relevant, a tag is fine, and if not, a Hausdorff tag is inappropriate.
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I don’t think that there should be a countability-axioms tag in the first place: it’s not a natural category. Second countability, first countability, and separability are just names for the countable cases of the cardinal functions weight, character, and density, respectively. If we do have it, ...

So in the light of the previous discussion, the reasonable way to handle this new tag is to simply replace it by . (At least if we follow what I quoted above from Brian M. Scott's answer.)

1 hour later…
4:25 PM
BTW the tag discussed above was removed. So we will see what is the result of discussion on meta - and if some kind of consensus is reached, a new tag can be created.