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How to understand the words 'upper' and 'lower' in the concepts 'upper hemi-continuous' and 'lower hemi-continuous'? I know for semicontinuity the words 'lower' and 'upper' have obvious geometric meanings. But does it seem that the words 'upper' and 'lower' in these two concepts are unrelated to location (like the daily meaning of these two words)?

Shujun Tan
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  • I would conjecture it's by analogy with lower and upper semicontinuity, which has a more geometric picture. Note this analogy is a rather weak one, so is just my guess: hemicontinuity nor semicontinuity are special cases of the other in general (hemicontinuity of a single valued function is just normal continuity, but can also be applied to set valued functions). – Brevan Ellefsen Mar 24 '23 at 22:03
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    I wonder why this post was downvoted for lack of clarity. May be you should repeat in the body of your post the question of your title, and insist on the fact that contrarily to what happens for semicontinuity for which things are clear to you, the words "upper" and "lower" do not have an obvious interpretation for hemicontinuity. – Anne Bauval Mar 24 '23 at 22:03

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