9.J. If A is any subset of R', let A denote the union of all open...

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9.J. If A is any subset of R', let A° denote the union of all open sets which are contained in A; the set A° is called the interior of A. Note that A° is an open set; prove that it is the largest open set contained in A. Prove that A°s A, (A°)° = A° (ANB)° = A°n B', (R')° = R°. Give an example to show that (A UB)° = A°UB° may not hold. 9.J. If A is any subset of R', let A° denote the union of all open sets which are contained in A; the set A° is called the interior of A. Note that A° is an open set; prove that it is the largest open set contained in A. Prove that A°s A, (A°)° = A° (ANB)° = A°n B', (R')° = R°. Give an example to show that (A UB)° = A°UB° may not hold.