Is it possible to remove the edge connecting point 4 and point 10 without altering the overall topological structure of the mesh?

No.
Polygons need a minimum of 3 sides connected in sequence to each other(to be seen as a surface plane). If you 'remove' that edge you are left with only 2 without any connection to each other.

If you set your viewport display to Smooth Shaded you will no longer see that edge.

This is why you might think in other apps they are able to do this, but it's just being hidden from you.

That edge is called a "bridge", it is essential for closed polygons with "holes" to still be a single polygon

Imagine drawing that polygon without lifting your pencil off of the paper, you would cross the bridge 2x to return to the starting point (same way bridge in your polygon is made of 2 half edges)

Without it you will get 2 polygons instead of 1 (as it is no longer possible to draw without lifting the pencil), like if you apply Hole SOP and check Un-Bridge Holes

BabaJ
No.
Polygons need a minimum of 3 sides connected in sequence to each other(to be seen as a surface plane). If you 'remove' that edge you are left with only 2 without any connection to each other.

If you set your viewport display to Smooth Shaded you will no longer see that edge.

This is why you might think in other apps they are able to do this, but it's just being hidden from you.

Yes, I think I've seen other software do this, but when I used two circles and the addvertex function to add points, I realized it might not be possible. Thank you for your explanation

tamte
That edge is called a "bridge", it is essential for closed polygons with "holes" to still be a single polygon

Imagine drawing that polygon without lifting your pencil off of the paper, you would cross the bridge 2x to return to the starting point (same way bridge in your polygon is made of 2 half edges)

Without it you will get 2 polygons instead of 1 (as it is no longer possible to draw without lifting the pencil), like if you apply Hole SOP and check Un-Bridge Holes

Thank you for your explanation