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open set (plural open sets)

  1. (topology) 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. (topology, analysis, restricted to metric spaces) 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. (topology) Most generally, a member of the topology of a given topological space.

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