To be a bit more precise an "open" bound is one which excludes the actual limit. So if we take the open interval (0, 1) on the Real Numbers we are looking at all Real Numbers greater than zero and less than one.
For any number in that range we choose we can find another that is closer to one and another that is closer to zero. One and zero are outside the range because we are using an open bound at each end and they are explicitly outside the interval.
If we choose 0.999, 0.9999 is closer to 1.
If we choose 0.001, 0.0001 is closer to 0.
In fact for any number, x, in the range that we choose (x+1)/2 will be closer to 1 and x/2 will be closer to 0.