Sets & Notations: What Do S* and S* Mean?

[RedGolpe]

I have seen different notations on different books but I couldn't find anywhere what S* and S_* mean, being S a set. Anyone can help?

 

[HallsofIvy]

Without knowing the context, I doubt if anyone can say. I can think of a few possiblities such as "upper Riemann sum" and "lower Riemann sum" for an integral or "push forward" and "pull back" of a morphism, but those don't apply just to "sets".

 

[RedGolpe]

Thank you for your quick answer. I doubt it to be anything more complicated than very basic set theory. Unfortunately, I don't know the context myself, all I have is a simple test asking to answer true or false to several questions:

if l belogs to A_* then l+1 does not belong to A_*;
if l belogs to A* then there exists an epsilon>0 such that l-epsilon belongs to A*.

I suspect it's something like "A together with its supremum/infimum" or something pretty straightforward like that. I just wanted to know if anyone had seen this notation before, as I can still ask the person who gave me those tests to show me his textbook.

 

[g_edgar]

The notation was surely explained just before the questions applying to it.

 

[RedGolpe]

Unfortunately not. As I said, this was a test sheet and I don't have access to the relevant textbook. Anyway I'd say it's obvious now that this is not standard notation, I'll check it on the book itself when it becomes available.

Edit: For all the curious here, I managed to obtain the textbook. A* is defined as the set of all the elements greater than all the elements in A. Similarly, A_* is the set of all the elements smaller than all the elements in A.