A 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 is more then one possible outcome of the discussion.)
The natural question concerning tagging questions about semicontinuous functions are:
- Should we have a separate tag for semicontinuity?
- If yes, should both lower and upper semicontinuity have separate tags or should they be under the same tag.
- If not, should we expand the scope of the continuity tag to include this topic. (After all, some users have been using the tag in this way. But it would be nice to know the consensus of the community about this. And if the consensus is that the questions about semicontinuity belong here, this should be mentioned explicitly in the tag info.)
- Should the tag include also semicontinuity of multifunctions?
You can see a short discussion in chat between me and the user who created (upper-semicontinuity). And also that the tag-creator would prefer to have separate tags for lower and upper semicontinuous tags.