I assume the origins of how it's called ties to the mathematical definition of open/closed sets (https://en.wikipedia.org/wiki/Open_set https://en.wikipedia.org

I assume the origins of how it's called ties to the mathematical definition of open/closed sets (https://en.wikipedia.org/wiki/Open_set https://en.wikipedia.org/wiki/Open_set). In an (imprecise) way, the closed set is a water balloon and the open set doesn't have the rubber balloon wrapping the water - I would consider the water balloon to be 'closed' in this case.