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Banach fixed-point theorem and List of general topology topics

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

Difference between Banach fixed-point theorem and List of general topology topics

Banach fixed-point theorem vs. List of general topology topics

In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points. This is a list of general topology topics, by Wikipedia page.

Similarities between Banach fixed-point theorem and List of general topology topics

Banach fixed-point theorem and List of general topology topics have 7 things in common (in Unionpedia): Cauchy sequence, Compact space, Complete metric space, Lipschitz continuity, Metric space, T1 space, Ultrametric space.

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.

Banach fixed-point theorem and Cauchy sequence · Cauchy sequence and List of general topology topics · See more »

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).

Banach fixed-point theorem and Compact space · Compact space and List of general topology topics · See more »

Complete metric 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).

Banach fixed-point theorem and Complete metric space · Complete metric space and List of general topology topics · See more »

Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.

Banach fixed-point theorem and Lipschitz continuity · Lipschitz continuity and List of general topology topics · See more »

Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

Banach fixed-point theorem and Metric space · List of general topology topics and Metric space · See more »

T1 space

In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other.

Banach fixed-point theorem and T1 space · List of general topology topics and T1 space · See more »

Ultrametric space

In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d(x,z)\leq\max\left\.

Banach fixed-point theorem and Ultrametric space · List of general topology topics and Ultrametric space · See more »

The list above answers the following questions

Banach fixed-point theorem and List of general topology topics Comparison

Banach fixed-point theorem has 25 relations, while List of general topology topics has 166. As they have in common 7, the Jaccard index is 3.66% = 7 / (25 + 166).

References

This article shows the relationship between Banach fixed-point theorem and List of general topology topics. To access each article from which the information was extracted, please visit:

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