metric space (Meaning)
metric space (n)
a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
Synonyms & Antonyms of metric space
No Synonyms and anytonyms found
metric space Sentence Examples
- The metric space provides a framework for quantifying distances between elements.
- The concept of a metric space is fundamental in various mathematical disciplines, including topology and analysis.
- In a metric space, the distance between any two points is nonnegative and symmetric.
- Metric spaces allow for the definition of notions such as convergence, completeness, and compactness.
- The Euclidean space is a well-known example of a metric space, where the distance is measured using the Euclidean distance formula.
- Abstract metric spaces generalize the Euclidean space by allowing for more abstract distance functions.
- The study of metric spaces has led to the development of important concepts such as the Hausdorff distance and the Gromov-Hausdorff distance.
- Metric spaces are used in diverse applications, ranging from computer science to physics.
- The Cauchy-Schwarz inequality is a fundamental result in metric spaces that relates the inner product of vectors to their distances.
- The concept of a metric space has been extended to non-commutative settings, giving rise to non-commutative metric spaces.
FAQs About the word metric space
a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequal
No synonyms found.
No antonyms found.
The metric space provides a framework for quantifying distances between elements.
The concept of a metric space is fundamental in various mathematical disciplines, including topology and analysis.
In a metric space, the distance between any two points is nonnegative and symmetric.
Metric spaces allow for the definition of notions such as convergence, completeness, and compactness.
