Unable to understand "Open Set" I keep reading the definition of an open set & neighborhood, but I just don't seem to get it. This is the defn - "a set U is open if any point x in U can be "moved" a small amount in any direction and still be in the set U." I don't see how this condition can ever be satisfied. For eg, after this, it typically says - "an open set is a solid region minus its boundary". I don't understand this because a solid region minus the boundary does have a boundary. It's just that the new boundary is slightly smaller as compared to the previous boundary i.e. I am not able to grok the concept of how a point at the edge of a region can be moved outwards and still remain in the region. Can someone explain this? Same thing with understanding "Neighbourhood of a point" also? Is there something else I need to study to understand this?