Exercise 32.1

Question

Show that a closed subspace of a normal space is normal.

Amit Awasthi · Accepted Answer

\begin{proof}
  Suppose $Y$ is our closed subspace of our normal space $X$, and $A,B \subseteq Y$ disjoint and closed. By Theorem 17.3, $A,B$ are closed in $X$. Let $U,V$ be a separation of $A,B$ in $X$. Then, $Y \cap U, Y \cap V$ separate $A,B$ in $Y$, and so $Y$ is normal.
\end{proof}

Exercise 32.1

Answers

Comments

Exercise 32.1

Answers

Comments

Add answer