Let A and B are subsets of a topological space (X, T).If A⊆B then Int(A)⊆Int(B).

Proof;

To prove that if A⊆B then Int(A)⊆Int(B), where A and B are subsets of a topological space (X, T), we will use the definition of interior of a set A and B.

By definition
Int(A)⊆ A and Int(B)⊆B

Let            A⊆B                               

⇒ Int(A)⊆A⊆B

⇒ Int(A)⊆B

⇒ Int(A)⊆Int(B)

∵ Int(A) is an open set which is contained in B but Int(B) is a largest open set which is contained in B.

Hence proved that If A and B are subsets of Topological Space (X, T) such that  A⊆B then  Int(A)⊆Int(B).