Let Y be a subspace of X and let A be a subset of Y. Denote by Cl(A_X) the closure of A in the topological space X and by Cl(A_Y) the closure of A in the topological space Y. Prove that Cl(A_Y) is a subset of Cl(A_X) . Show that in general Cl(A_Y) not equal Cl(A_X). See the attached file.© BrainMass Inc. brainmass.com October 10, 2019, 1:46 am ad1c9bdddf
A proof of the fact that the closure of a set in a topological subspace is a subset of the cosure of the same set in a bigger space is given. A counterexample to the equality claim is given. The solution is in a PDFfile.