A metric space is a set together with a notion of distance between its points, called a metric, which must satisfy that the distance from a point to itself is zero, the distance between two different points is always positive, distance is symmetric, and the triangle inequality holds. The idea of an abstract space with metric properties was addressed in 1906 by Maurice Frechet, and the term metric space itself was coined by Felix Hausdorff in 1914. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Compact Space, Concepts Compactness was first formulated for spaces of functions with a distance notion (Frechet, 1906) and in a metric space it coincides with the space being both complete and totally bounded, the classical form of the concept.
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a metric space is a set together with a notion of distance between its points
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The idea of an abstract space with metric properties was addressed in 1906 by Rene Maurice Frechet and the term metric space was coined by Felix Hausdorff in 1914.
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Wikimedia FoundationAssociated With: Compact Space, Lead sectionQuote, Associated With: Compact Space, Lead section
compactness is a property of a space that makes it behave in many ways like a finite set
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