"sup" in functional analysis

[a_ronagh]

Hi

I have encountered an abbreviation "sup" in an article
just as below:

d(x,y)=sup|x(t)-y(t)|

What does "sup" stands for in functional analysis?
I am a beginner in this issue.Please explane it a little.

Thank you so much.

 

[main_road]

sup means "least upper bound".

 

[maple]

"SUP" is a concept in functional analysis, which means: the least one still larger than the element in the set you concerned.