newPopUp = window.open();
//Code for if Pop-Up has been closed.
//Code for if pop-up is still open.
The key here then is that when the pop-up is initialised, it needs to be given a name by which its status can be checked. In this case the name is newPopUp. If it has indeed be closed newPopUp.closed will return true, and if not it will return false.
Here is a more extensive code example, with the current status of the pop-up being written into a span via getElementById():
<title>Check Pop-Up Status</title>
newPopUp = window.open("", "", "width=300, height=150");
newPopUp.document.write("Your text here");
var status = document.getElementById("status");
status.innerHTML = "PopUp has been closed.";
status.innerHTML = "PopUp is still open.";
<input type="button" value="Open Pop-Up" onclick="javascritp:popup()" />
<input type="button" value="Check Status" onclick="javascritp:popUpStatus()"><br>