## OPENSET

### Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line. The simplest generalization is in metric spaces, where open sets can be defined as those sets which contain an open ball around each of their points . However, an open set in general can be very abstract: any collection of sets can be called open as long as the union of an arbitrary number of open sets is open, the intersection of a finite number of open sets is open, and the space itself is open. These conditions are very loose, and they allow enormous flexibility in the choice of open sets. In the two extremes, every set can be open, or no set can be open ...

The above text is a snippet from Wikipedia: Open set

### open set

#### Noun

1. 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.
2. 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.
3. Most generally, a member of the topology of a given topological space.

The above text is a snippet from Wiktionary: open set