open set

An "open set" is a fundamental concept in topology and other areas of mathematics, crucial for understanding properties like continuity and convergence.

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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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