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underlying set

mathematic

The "underlying set" forms the basis for various mathematical structures, such as topological spaces and algebraic structures.

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Definition

C1General

(technical)The basic collection of elements that serves as the foundation for a mathematical structure or system.

Example

  • Different mathematical structures can be built on the same underlying set of elements.

C1Topology

(technical)A set of points on which a topology is defined, creating a topological space.

Example

  • In topology, the underlying set is crucial for defining the properties of a topological space.

C1Algebra

(technical)A set of elements on which algebraic operations are defined, forming an algebraic structure.

Example

  • The underlying set of a group consists of its elements along with the group operation.

C1Metric Spaces

(technical)A set of points for which a distance metric is defined.

Example

  • The underlying set of a metric space allows for the definition of distances between points.

Similar

Terms that have similar or relatively close meanings to "underlying set":

level setset theoryitem setdata setopen setordered setdisjoint set