metric space (Meaning)

Wordnet

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

  1. The metric space provides a framework for quantifying distances between elements.
  2. The concept of a metric space is fundamental in various mathematical disciplines, including topology and analysis.
  3. In a metric space, the distance between any two points is nonnegative and symmetric.
  4. Metric spaces allow for the definition of notions such as convergence, completeness, and compactness.
  5. The Euclidean space is a well-known example of a metric space, where the distance is measured using the Euclidean distance formula.
  6. Abstract metric spaces generalize the Euclidean space by allowing for more abstract distance functions.
  7. The study of metric spaces has led to the development of important concepts such as the Hausdorff distance and the Gromov-Hausdorff distance.
  8. Metric spaces are used in diverse applications, ranging from computer science to physics.
  9. The Cauchy-Schwarz inequality is a fundamental result in metric spaces that relates the inner product of vectors to their distances.
  10. 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.