Concept information
Terme préférentiel
compactness
Définition(s)
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In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact. Similarly, the space of rational numbers Q is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers R is not compact either, because it excludes the two limiting values + ∞ and − ∞. However, the extended real number line would be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topological spaces.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Compact_space)
Concept(s) générique(s)
Synonyme(s)
- compact space
Traductions
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français
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espace compact
URI
http://data.loterre.fr/ark:/67375/PSR-MPQHSB53-6
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