The question comes from “Introduction to Topology: Pure and Applied” by Colin Adams and Robert Franzosa.
I have very little knowledge of set theory and proofs, so I'm not sure how to prove this. As always, I appreciate any help.
Some definitions from the textbook:
Let A be a subset of a topological space X. The interior of A, denoted Å or Int(A), is the union of all open sets contained in A. The closure of A, denoted Ā or Cl(A), is the intersection of all closed sets containing A.
∂A = Cl(A) − Int(A)
∂A = Cl(A) ∩ X – Int(A)
∂A = Cl(A) ∩ Cl(X − A)
"Let A be a subset of a topological space X. Prove that ∂A ∪ Int(A) = Cl(A)"