To check if a stroked contour is "open" (meaning the start and end points are not joined) in Adobe Illustrator, you can use several methods depending on how many objects you are checking. This is a critical step for your print-on-demand and large-format work to ensure cutting heads follow a continuous path.
1. The Document Info Panel (Most Reliable)
This is the fastest way to get a definitive count of open vs. closed paths.
Select your suspected open contour.
Go to Window > Document Info.
Click the panel menu (three lines in the top right) and select Objects.
Look for the line that says Paths. It will explicitly state how many are Open and how many are Closed.
2. The "Join" Test
If you suspect a path is open, you can attempt to force it closed:
Select the object.
Press Command + J (Mac) or Ctrl + J (Windows).
If a new segment appears between two points, the path was open. If Illustrator tells you "To join, you must select two end points," the path is already closed or complex.
3. Using "Select Next Object" (For Single Paths)
Select the path with the Selection Tool (V).
If you look at the path in Outline Mode (Command + Y (Mac) or Ctrl + Y (Windows)), zoom in on the start/end point.
Use the Direct Selection Tool (A) to click and drag a single anchor point. If the path "breaks" apart, it is not joined.