$\displaystyle X=\{(x,0) : 0\leq x\leq1\} $

i think it is closed, if we define a sequence : $\displaystyle x_{n}\in X, x_{n}=(\frac{1}{n},0)\rightarrow x=(0,0)\Rightarrow x\in X. $

i hope my definition of closed subset is right. Maybe my result is wrong coz i choose a special case.

another question ,what about $\displaystyle X=\{ (x,0) : 0<x<1\} $