Exercise 2.2.5

Question

Let $X$ be a topological space and let $S$ be a subset of $X$. Show that if $A$ is a relatively open subset of $S$, then $A \cap T$ is a relatively open subset of $S \cap T$ for any subset $T$ of $X$.

Elu Thingol · Accepted Answer

\begin{proof}
Since $A$ is relatively open in $S$, there is an open set $U$ of $X$ such that $A = U \cap S$. The theorem assertion then follows straightforward from
$$A \cap T = (U \cap S) \cap T = U \cap (S \cap T).$$
\end{proof}

Exercise 2.2.5

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Exercise 2.2.5

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