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Let X be a metric space and let E C X. The boundary aE of E is defined by E EnE (a) Prove that DE = E\ E°. Here Eo is the set

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la) To Sho that let 2eE ndE Claim t is eE Ahen 3 S0 s- imit Point os So is seauen ce n3 SESt n So Bs(a) aondains infinuteny mis open ) let a33e eis opem so = ExE el 1EENBE EDE and z eE 1et open Ss et 0 15 not 3o EE 3 EE E Sucn that OPen So Poss ou leTS Possible let 3 eE such that f E EE xe En E >1 3E 36 eE 2EE 2 EE Hen ce ECE . E E E is c osed X1R 2 aAn a R n IR 11

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