File:Red_blue_circle.svg · Wikimedia Commons · See Wikimedia Commons
open set
Sign in to saveAlso known as open subset
set that does not contain any of its boundary points
~26 min read
Article
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.
Connections
continuous function
Entity
metric space
Entity
real number
Entity
interval
Entity
topological space
Entity
image
Entity
Euclidean distance
Entity
compact space
Entity
interior
Entity
uniform space
Entity
International Standard Book Number
Entity
circle
Entity
mathematical analysis
Entity
function
Entity
topology
Entity
rational number
Entity
set
Entity
point
Entity
empty set
Entity
OCLC, Inc.
Entity