open set
An "open set" is a fundamental concept in topology and other areas of mathematics, crucial for understanding properties like continuity and convergence.
Definition
C2Topology
(technical, academic)A collection of points where each point has a neighborhood fully contained within the collection.
Example
- In topology, the concept of an open set helps define continuous functions.
C2Metric Spaces
(technical, academic)A group of points such that for every point, there is a surrounding region that is entirely within the group.
Example
- An open set in a metric space ensures that you can always find a small enough radius around any point that stays within the set.
C2General Topology
(technical, academic)A member of a collection of sets that includes the whole space, the empty set, and is closed under unions and finite intersections.
Example
- In general topology, the open sets form the building blocks of the topological space.
Similar
Terms that have similar or relatively close meanings to "open set":
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