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1:14 PM
Still about semicontinuity:
I'm afraid this answer does not get the exposure it deserves here. — Asaf Karagila 3 hours ago
@AsafKaragila To be honest, that is probably true for any of the answers in this thread. But if you think that it is a good idea, feel free to go ahead and start a separate question about this. (Or simply try to badger me a bit until I do so, if that's the preferred course of action.) — Martin Sleziak 33 secs ago
@MartinSleziak Since there were no objections here in chat, I wen ahead and removed hausdorff-spaces tag.
 
1:31 PM
1
Q: Tag for semicontinuity?

Martin SleziakA few days ago the tag upper-semicontinuity was created and later removed. This lead to a discussion about this tag in the tag management thread. As suggested by Asaf, it might be more reasonable to discuss this in a separate question. (Among other reasons, there are more then one possible outcom...

 
@AlexRavsky As you can see above, the discussion now has moved to a separate question.
I just wanted to let you know about this - in case you want to joint the discussion on meta.
@AsafKaragila I am pretty sure you will notice the new post on meta, but I'll ping you just in case to let you know that now there is a separate posts about semicontinuity.
There is already enough comments under the answer in the tag-management thread - which is the reason why I pinged you in chat instead of adding a new comment.
 
1:57 PM
@MartinSleziak Who do you think cast the first vote on the question? (Not taking stance on the answer just yet.)
 
That was my guess.
Of course, votes are anonymous, so I couldn't be sure.
 
 
6 hours later…
7:34 PM
The problem with using the same tag for semicontinuous functions and semicontinuous multifunctions is that the terminology is inconsistent here. If we identify a function with a multifunction that happens to have singletons as values, the function is upper-semicontinuous as a multifunction iff it is lower-semicontinuous as a multifunction iff it is continuous as a function. Indeed, that is the reason why many people (including me) prefer to talk about hemicontinuity in the case of multifunctions. — Michael Greinecker ♦ 1 hour ago
@MichaelGreinecker As I said, I am pretty sure that both names are commonly used for multifunctions. Your suggestion would be to have a separate (hemicontinuity) tag - which would be for multi-valued functions? — Martin Sleziak 1 hour ago
@MartinSleziak Yes, I would have a tag for semicontinuous functions, but not multifunctions. I don't know whether we need to have a hemicontinuity tag for multifunctions, but I don't think we should have an umbrella talk for clearly distinct concepts. It would be like having a "regular" tag that covers every use of regularin mathematics. — Michael Greinecker ♦ 31 mins ago
@MichaelGreinecker It is a valid point. (Although I think that using the same tag for corresponding notions for functions and multifunctions is much less extreme than you example with "regular".) Why not posting a separate answer suggesting a tag that would exclude multifunctions. (So that it is possible to vote on that suggestion and see what other users thing about these two suggestion.) — Martin Sleziak 4 mins ago
@MartinSleziak I interpreted your suggestion of having a tag for"semicontinuous functions" to already exclude multifunction. The regular case is of course extreme, but it was my impression that similarly named but distinct concepts should have distinct tags. — Michael Greinecker ♦ 1 min ago
@MichaelGreinecker Since this is getting a bit too long, why don't we continue the discussion in chat. — Martin Sleziak just now
It seems that I expressed it somewhat unclearly, but my original suggestion was to have a tag which would include both functions and multifuctions.
My main concern - and the reason why I suggested to make a separate answer - is that there are already three upvotes for the current version. (Which was the suggestion to include both functions and multifunctions.)
So this would feel a bit like changing in the middle of voting the "poll question".
Of course, we do not know whether the suggestion to include multifunctions influenced these votes that much. (Most likely not.)
 
@MartinSleziak One upvote was by me, under the impression that it applies to functions.
 
Fair enough.
That clears up at least one of them.
I guess one might be from Vim, who clearly stated in a comment that they do not care that much about hemicontinuity.
I agree with you that it's favourable to create a single semicontinuity tag. Also there's no need to create separate "upper/lower SC" tags because it's just a matter of the sign, at least in the real-valued case. I don't know much about hemicontinuity, but I guess it won't have many related posts anyway. — Vim 1 hour ago
I am open to both actions - depending on what you say.
I can edit my post to exclude multifuctions.
If we assume that at least two votes were by users who do not care about multi-valued maps (or are even against including them) this does not change much.
The other possibility is that I keep my answer the way it is (or perhaps stress a bit more that it includes multifunctions) and you post a separate answer.
 
I think this is a good solution, that would also allow for some separation between upvoting commentary and the poll aspect.
 
There might be some other people like me which are used to see term semicontinuity quite commonly in either of the two context. So maybe the tag name might be a bit clearer that .
@MichaelGreinecker Ok, so you are going to post a new answer and I will stress a bit more in my answer that it includes multifunctions?
 
@MartinSleziak Yes, I will make that distinctive difference. I agree that "semicontinuous-functions" is better than "semicontinuity". Btw: Could you remind me what the markdown for tags is?
 
7:45 PM
It is [tag:tagname] - .
 
Thank you!
 
For tags on meta [meta-tag:tagname].
I have edited my answer a bit - I hope it is now clearer that my suggestion is to include also multi-valued maps.
The edit also makes it possible for you to remove the upvote - which you probably already did :-)
One of the reasons why I was originally inclined to include both meanings is that I see semicontinuity of multifunctions quite often. (But it might be simply the case that I happen to read some stuff which uses less standard terminology.)
You arguments seem to me quite reasonable. So it's quite possible that after I think about it a bit, I might upvote your answer. (Despite the fact that I originally came up with a different suggestion.)
And, of course, thanks for joining the discussion about the new tag!
BTW only now I notice that when Alex Ravsky created the original tag, he only mentioned functions in the tag-excerpt.
 
Yes, that was my vote. I think there is some variation across fields. General topologists seem to prefer semicontinuity and mathematical economists and optimization theorists hemicontinuity, but the treatment is not uniform.
 
That might be an explanation. People I usually talk to about stuff like this are general topologists.
I am not sure what about analysts. But maybe you would count Aliprantis as economist rather than analyst.
Wikipedia says that he was an economist and mathematician.
 
Aliprantis uses hemicontinuity in his textbook with Kim Border. He turned to economics after coming to the US when economists Donald Brown started working with him. Jean-pierre Aubin seems to prefer semi-continuity, which suggest that the term is acceptable for nonlinear analysts who need both concepts.
 
8:00 PM
Thanks for posting the answer!
 
Thanks for taking care of all things tagging!
 
To be honest, I mainly reacted to the newly created tag.
My main objection to creation of was that having two separate tags for upper and lower semicontinuity seemed to specific to me. That eventually lead to the post(s) on meta.
 
We are in agreement there. Dual concepts don't need dual tags.
 
I'm going to grab something to eat. See you later!
 
See ypu and bon appetite!
 

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