open set
Also known as open subset
set that does not contain any of its boundary points
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Example: the blue circle represents the set of points (x, y) satisfying x + y = r. The red disk represents the set of points (x, y) satisfying x + y < r. The red set is an open set, the blue set is its boundary set, and the union of the red and blue sets is a closed set.
In general topology and mathematical analysis, an open set is a generalization of an open interval in the real line.