[kanji]

อีกชุด ครับ
1.Prove that $A$ is dense in $X$ if and only if $\overline{A} =X$. where $\overline{A} $ = closure of $A$.
2.Prove that $Q$ and $R-Q$ are dense in $R$.
3.A point $p$ is an element of $\overline{A}$ if and only if for every positive real number $r$, $N_r(p)\cap A\not= \emptyset $.
4.Prove that $X$ is connrcted if and only if $X$ has exactly two subsets which are both open and closed in $X$.
5.Let $X$ be any nonempty set and $d$ the discrete metric on $X$. Prove that every subset of $X$ is open and every subset is closed.