Sentence Correction

Hi, there!

I have a correct sentence here, and I have no idea what's the meaning of "such that"here. Can someone help me figure it out? Thank you very much!

A rule of correspondence between two sets such that there is a unique element in the second set assigned to each element in the first set. (the interpretation says such refers to "a rule of ... sets" )

Thank you very much for help!

such that often begins a definition.

In the sentence you cited, you could replace such that with having the quality.

A rule...having the quality there is a unique element in the second set assigned to each element in the first set

Here is another use of such that.

John's test anxiety was such that it affected his performance.

So the anxiety affected his performance. If the anxiety had been different it would not have affected his performance, but the anxiety was such that, of a kind that, or a degree of anxiety that affected his performance.

Such that is often used in math. Here it is in a GMAT question.

x and y are positive integers such that x=8y+12...

So x and y are positive integers having the quality x=8y+12.