Empty sets can only be transformed into topological spaces in one way, that is, by defining empty sets as open sets; This empty topological space is the only initial object of topological space category with continuous mapping.

An empty set is the proper subset of any non-empty set. ? There is only one subset, and there is no proper subset. {? } has two subsets, one is? One is itself.

Introduction to empty set representation;

Use symbols? Or {} means.

Note: {? } Is there? A collection of elements, not an empty set. In LaTeX, an empty set represents the code \emptyset.

0 is a number, not a set. {0} is a collection with only element 0. ? Is a collection, but does not contain any elements.

{? } is a non-empty set, and the set has only elements of an empty set.

Extended data:

Introduction to the properties of empty sets

1. For any set A, an empty set is a subset of A:? A: a;

2. for any set a, the union of empty set and a is a:? A: A ∨? = A；

3. For any nonempty set A, the empty set is the proper subset of A:? A,,, If A≦? And then what? Really contained in a.

4. for any set a, the intersection of an empty set and a is an empty set:? One, one? = ? ;

5. For any set A, the empty set and the cartesian product of A are all empty sets:? One, one ×? = ? ;

6. The only subset of an empty set is the empty set itself:? A, if a? A, so A= ; ? A, if A=? So a? Answer.

7. The number of elements in an empty set (i.e. its potential) is zero;

8. Especially the empty set is limited: |? | = 0;

9. For a complete set, the complement of an empty set is a complete set: CU? =U .