**A space $X$ is called left-separated if it can be well-ordered in such a way that every initial segment is closed in $X$.**


Could someone post some left-separated space to help me understand such definition?



Understanding the left-separated spaces
This is just filling in some details of Ramiro de la Vega's comment: Given any space $X$, form a (possibly transfinite) sequence of points by the following induction. As long as (the range of) the sequence you've built so far isn't dense in $X$, choose arbitrarily a point not in its closure, and append the chosen point to your sequence. Stop only when your sequence has become dense in $X$. Every initial segment of (the range of) your sequence is closed because, after it was formed, you only added points outside its closure. 


