open set
Informally, a set such that the target point of a movement by a small amount in any…Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.
» You have three minutes for your open mic set.
Meaning
3 sensesInformally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.
A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set.
offene Menge
откры́тое мно́жествоotkrýtoje mnóžestvo
Most generally, a member of the topology of a given topological space.
Examples
2 sentencesYou have three minutes for your open mic set.
In a Fréchet space, the countable intersection of open dense sets is itself dense.
У просторі Фреше, зліченний перетин відкритих щільних множин є також щільним.