Let Y be a subspace of X and let A be a subset of Y. Denote by Int_X(A) the interior of A in the topological space X and by Int_Y(A) the interior of A in the topological space Y. Prove that Int_X(A) is a subset of Int_Y(A). Illustrate by an example the fact that in general Int_X(A) not Int_Y(A).© BrainMass Inc. brainmass.com October 10, 2019, 1:46 am ad1c9bdddf
The proof of the fact that the interior of a set with respect to a topological space is a subset of the interior of the same set with respect to a topoogical subset if presented. A counterxample to the general equaligy is given. The solution is in a PDF file.