Complete works: Generally speaking, if a set contains all the elements involved in the problem we are studying, it is called complete works, usually denoted as U.

Basic set: Basic set is one of the important invariant sets in the study of dynamic systems. It is an abstract concept based on the dynamic nature of the basic set of spectral decomposition of axiomatic A system.

Related information:

Once a given set is considered. A subset of x (in Cantor's case, X=? R), you will be more concerned about the set of subsets of X. (For example, is a topology on X a topology? A set of subsets of X. The set of these different subsets of x is not a subset of x itself, but it is? A subset of the power set PX of x?

Of course, this is not over yet; Can you reconsider? A set of subsets of x, and so on. The other direction is: you can care about cartesian product X×? X, or map from x to your own function. Then, you can get the function on the Cartesian product, or map from x to x? The function of PX, and so on.