Q 69. - Calculus

Question

Let S be a subset of $R^2 or R^3$. Prove that$\partial (\partial S)\subseteq \partial S$
 

Step-by-Step Solution

Answer

It is proved that if S is the subset then $\partial (\partial S)\subseteq \partial S$

Step 1. Given information.

We have given S is a subset  of $R^2 or R^3$.

Step 2: Prove the given statement.

It is already proved that $\partial S$ is a closed set.

Substitute $\partial S$ for A in the theorem which states that for every closed set A, $\partial A\subseteq A$.

Thus, $\partial (\partial S)\subseteq \partial S$