 We also discuss the setting in which guards are open (i.e., they are segments without the endpoints), proving that the same results hold even in this more challenging case.
<clarity>  We also discuss the setting in which guards are open (i.e., they are segments without the endpoints), proving that the same results hold even in this more challenging case.
 We also consider the setting in which guards are open (i.e., they are segments without the endpoints), proving that the same results hold even in this more challenging case.