How supposed I imagine the following equations?

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The discussion centers around the concept of an open subset in R^n and its relationship to functions. It clarifies that a function u maps elements from an open subset U to real numbers, indicating that U is a subset of another set P. The key point is that for every element x in U, it must also belong to P. The participants seek to understand the implications of being an element of an open set in R^n. Overall, the conversation emphasizes the nature of functions and subsets in mathematical contexts.
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What is SUBSET on “open subset of R^{n}"?
How supposed I imagine the following equations?

u : U → R
 
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it's the same as any other subset.

U is a subset of P if

for all x in U x is also in P.

So what does it mean to be an element of an open set of R^n?

u is probably a function.

It assigns each element in U to one element in R
 

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