9.L. If A is any subset of R', let A denote the intersection of all closed...

Transcribed Image Text:

9.L. If A is any subset of R', let A denote the intersection of all closed sets containing A; the set A is called the closure of A. Note that A is a closed set prove that it is the smallest closed set containing A. Prove that (A) A ACA (A UB) A UB Give an example to show that (AnB) A-nB may not hold 9.L. If A is any subset of R', let A denote the intersection of all closed sets containing A; the set A is called the closure of A. Note that A is a closed set prove that it is the smallest closed set containing A. Prove that (A) A ACA (A UB) A UB Give an example to show that (AnB) A-nB may not hold