Let (X,T) be a topological space and suppose that A and B are subsets of X then (Int(A)∪Int(B))⊆Int(A∪B).


As we know 

A⊆(A∪B) and B⊆(A∪B)

⇒ Int(A)⊆Int(A∪B) and In(B)⊆Int(A∪B)

∵ If A⊆B then Int(A)⊆Int(B)

⇒ (Int(A)∪Int(B))⊆Int(A∪B) 

∵ If A⊆C and B⊆C then (A∪B)⊆C

Hence proved that (Int(A)∪Int(B))⊆Int(A∪B), where A and B are subsets of a topological space (X, T).

Noman Yousaf

Meet Noman Yousaf, a Math graduate from University of Education Lahore Jauharabad Campus. He excels at simplifying complex math topics, teaching with clarity and making math understandable for all.

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