METRIC SPACE Meaning and
Definition
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A metric space is a mathematical construct formed by combining a set of elements with a distance function, also known as a metric. It is a fundamental concept in the field of mathematics, particularly in the branch of topology.
In a metric space, the set of elements can be anything – numbers, points, sequences, or even other mathematical objects. The distance function, which is often denoted by d(x, y), assigns a non-negative real number to every pair of elements (x, y) in the set. It satisfies a few key properties: non-negativity (the distance between any two elements is always greater than or equal to zero), symmetry (the distance between x and y is the same as the distance between y and x), and the triangle inequality (the distance between x and z is always less than or equal to the sum of the distances between x and y and between y and z).
Metric spaces allow for the study of concepts such as convergence, continuity, and completeness. They provide a framework to explore distance-based relationships between elements in various mathematical contexts. By defining and investigating metrics, mathematicians can analyze the properties and behaviors of objects within a given space. For example, in the real numbers with the standard Euclidean metric, a metric space enables the measurement of distances between two points, opening the door to understanding concepts like length, diameter, and proximity.
Common Misspellings for METRIC SPACE
- netric space
- ketric space
- jetric space
- mwtric space
- mstric space
- mdtric space
- mrtric space
- m4tric space
- m3tric space
- merric space
- mefric space
- megric space
- meyric space
- me6ric space
- me5ric space
- meteic space
- metdic space
- metfic space
- mettic space
Etymology of METRIC SPACE
The word "metric" in "metric space" comes from the Greek word "metrikos", which means "relating to measure". The term "metric space" was introduced by the German mathematician Felix Hausdorff in 1914, and it refers to a mathematical structure where distances between elements are defined and can be measured. The term "metric" emphasizes the concept of measuring distances within the space.
Similar spelling words for METRIC SPACE
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