Open Set

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An open set is a set for which every point in the set has a neighborhood lying in the set. An open set is the complement of a closed set and. An open interval is an example of an open set.

Open set is a college-level concept that would be first encountered in a topology course covering point-set topology.


Interval: An interval is a connected piece of the real number line which may be open or closed at either end.


Neighborhood: The neighborhood of a point is an open set containing that point.
Set: In mathematics, a set is a finite or infinite collection of objects in which order has no significance and multiplicity is generally also ignored.
Topological Space: A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set.

Classroom Articles on Point-Set Topology

  • Closed Set
  • Point-Set Topology
  • Homeomorphism
  • Subspace

  • Classroom Articles on Topology (Up to College Level)

  • Dimension
  • Projective Plane
  • Metric
  • Projective Space
  • Metric Space
  • Topology
  • Möbius Strip
  • Torus