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Chapter 12: Q 69. (page 932)

Let S be a subset of R2orR3. Prove that鈭�(鈭�S)鈯�鈭�S

Short Answer

Expert verified

It is proved that ifS is the subset then鈭�(鈭�S)鈯�鈭�S

Step by step solution

01

Step 1. Given information.  

We have givenS is a subset ofR2orR3.

02

 Prove the given statement. 

It is already proved that 鈭�Sis a closed set.

Substitute 鈭�S for A in the theorem which states that for every closed set A, 鈭�A鈯�A.

Thus,鈭�(鈭�S)鈯�鈭�S

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