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Closure (topology) and Hilbert space

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Closure (topology) and Hilbert space

Closure (topology) vs. Hilbert space

In mathematics, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

Similarities between Closure (topology) and Hilbert space

Closure (topology) and Hilbert space have 14 things in common (in Unionpedia): Closed set, Closure (topology), Complex number, Dense set, Euclidean space, If and only if, Infimum and supremum, Limit point, Mathematics, Metric space, Open set, Partially ordered set, Real number, Sequence.

Closed set

In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.

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Closure (topology)

In mathematics, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Dense set

In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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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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Infimum and supremum

In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.

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Limit point

In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.

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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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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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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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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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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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The list above answers the following questions

Closure (topology) and Hilbert space Comparison

Closure (topology) has 44 relations, while Hilbert space has 298. As they have in common 14, the Jaccard index is 4.09% = 14 / (44 + 298).

References

This article shows the relationship between Closure (topology) and Hilbert space. To access each article from which the information was extracted, please visit:

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