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21 relations: Ball (mathematics), Closeness (mathematics), Euclidean distance, Filter (mathematics), If and only if, Interior (topology), Interval (mathematics), Mathematician, Mathematics, Metric space, Natural number, Neighbourhood system, Open set, Real line, Real number, Set (mathematics), Subset, Topological space, Topology, Tubular neighborhood, Uniform space.
Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Closeness (mathematics)
Closeness is a basic concept in topology and related areas in mathematics.
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Euclidean distance
In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.
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Filter (mathematics)
In mathematics, a filter is a special subset of a partially ordered set.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Interior (topology)
In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Neighbourhood system
In topology and related areas of mathematics, the neighbourhood system, complete system of neighbourhoods, or neighbourhood filter \mathcal(x) for a point x is the collection of all neighbourhoods for the point x.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Tubular neighborhood
In mathematics, a tubular neighborhood of a submanifold of a smooth manifold is an open set around it resembling the normal bundle.
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Uniform space
In the mathematical field of topology, a uniform space is a set with a uniform structure.
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Epsilon neighborhood, Epsilon-neighborhood, Neighborhood (mathematics), Neighborhood (topology), Neighbourhood (topology), Open neighborhood, Open neighbourhood, Punctured neighborhood, Punctured neighbourhood, Topological neighborhood, Topological neighbourhood.
References
[1] https://en.wikipedia.org/wiki/Neighbourhood_(mathematics)
