Assignment:
Let Fr(A) denote the frontier set of A and Cl(A) denote the closure of A, where A is a subset of R^n. Solve the following problems.
Q1. For any set A, Fr(A) is closed.
Q2. If A and B are any sets, prove that Cl(A and B) belongs to Cl(A) and Cl(B). Give an example where Cl(A and B) is empty, but Cl(A) and Cl(B) is not empty.
Q3. Show that x is the only limit point of the sequence constructed in Theorem 2.11.
Q4. Prove that the composition of two continuous functions is continuous.
Provide complete and step by step solution for the question and show calculations and use formulas.