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Complete metric space and Fréchet space

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

Difference between Complete metric space and Fréchet space

Complete metric space vs. Fréchet space

In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.

Similarities between Complete metric space and Fréchet space

Complete metric space and Fréchet space have 14 things in common (in Unionpedia): Absolute value, Baire category theorem, Banach space, Cauchy sequence, Compact space, Continuous function, Countable set, Euclidean space, Inverse function theorem, Locally convex topological vector space, Normed vector space, Product topology, Topological space, Topological vector space.

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

Absolute value and Complete metric space · Absolute value and Fréchet space · See more »

Baire category theorem

The Baire category theorem (BCT) is an important tool in general topology and functional analysis.

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Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.

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Cauchy sequence

In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.

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Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

Complete metric space and Continuous function · Continuous function and Fréchet space · See more »

Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

Complete metric space and Countable set · Countable set and Fréchet space · See more »

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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Inverse function theorem

In mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood of a point in its domain: namely, that its derivative is continuous and non-zero at the point.

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Locally convex topological vector space

In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.

Complete metric space and Locally convex topological vector space · Fréchet space and Locally convex topological vector space · See more »

Normed vector space

In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined.

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Product topology

In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.

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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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Topological vector space

In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.

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The list above answers the following questions

Complete metric space and Fréchet space Comparison

Complete metric space has 76 relations, while Fréchet space has 55. As they have in common 14, the Jaccard index is 10.69% = 14 / (76 + 55).

References

This article shows the relationship between Complete metric space and Fréchet space. To access each article from which the information was extracted, please visit:

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