File:Red_blue_circle.svg · Wikimedia Commons · See Wikimedia Commons
open set
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set that does not contain any of its boundary points
Wikidata facts
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- opposite of
- closed set
- does not have part
- boundary
- studied by
- topology
- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- maintained by WikiProject
- WikiProject Mathematics
Sources (3)
via Wikidata · CC0
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Encyclopedic overview
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.
Excerpted from Wikipedia’s “open set” article, available under the CC BY-SA 4.0 licence.