Question: Let (X , d) be a metric space and E a nonempty subset of X. An element r E X is said to be on

Let (X , d) be a metric space and E a nonempty subset of X. An element r E X is said to be on the boundary of E if every neighbourhood NT($) of x contains a point in E and a point not in E. The set consisting of the boundary points of E is denoted by 8E. Prove (a) E is closed if and only if (9E Q E. (b) E is open if and only if E 0 8E : (Z). (c) E=EU8E

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