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Chapter 12: Q 67. (page 932)

Let S be a subset of R2or R3. Prove that 鈭�S=鈭�Sc

Short Answer

Expert verified

The given statement is proved if S is the subset then鈭�S=鈭�Sc.

Step by step solution

01

Step 1. Given information. 

We have givenS is a subset ofR2orR3.

02

 Prove the given statement.   

Assume an elementx'such that x鈭�鈭�S.

This means that the element 'x'is on the boundary of S.
Every open disk D around this element 'x' will extend to both SandSc.
Hence, 'x' should be included in the boundary of Scalso.
Thus,x鈭�鈭�Sc
Combine both the statements,

鈭�S=鈭�Sc

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