The empty set is open because the statement: "if x in A, some neighborhood of x is a subset of A" is true!
If A is empty, the hypothesis: "if x in A" is false and so the statement is vacuously true.
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Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.
The empty set is a set that has no elements.
The only subset of an empty set is the empty set itself.
An empty set is a set with no elements. It can be symbolized by {} or ø. The solution set for an equation that has no solution is also called an empty set.
An empty set in math is called a null set.