En topologie, un point x d'un espace topologique E est dit isolé si, intuitivement, il y a discontinuité en x (de tout côté) ; s'il n'a pas de voisin "collé" à lui.

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  • En topologie, un point x d'un espace topologique E est dit isolé si, intuitivement, il y a discontinuité en x (de tout côté) ; s'il n'a pas de voisin "collé" à lui. Techniquement, x est isolé si le singleton {x} est un ensemble ouvert.Formulations équivalentes :{x} est un voisinage de x ; x n'est pas adhérent à E\{x} (x n'est pas un « point d'accumulation »).En particulier si E est un espace métrique (par exemple une partie d'un espace euclidien), x est un point isolé de E s'il existe une boule ouverte centrée en x qui ne contient pas d'autre point de E.Un espace topologique dans lequel tout point est isolé est dit discret.
  • In topology, a branch of mathematics concerning the study of shapes and spaces, a point x of a topological space X is called an isolated point of a subset S of X if x belongs to S and there exists in X a neighborhood of x not containing other points of S. This is equivalent to saying that the singleton {x} is an open set in the topological space S (considered as a subspace of X).In particular, in a Euclidean space (or in a metric space), x is an isolated point of S, if one can find an open ball around x which contains no other points of S.Equivalently, a point x in S is an isolated point of S if and only if it is not a limit point of S.A set which is made up only of isolated points is called a discrete set. Any discrete subset of Euclidean space is countable, since the isolation of each of its points (together with the fact the rationals are dense in the reals) means that it may be mapped 1-1 to a set of points with rational co-ordinates, of which there are only countably many. However, a set can be countable but not discrete, e.g. the rational numbers with the absolute difference metric. See also discrete space.A set with no isolated point is said to be dense-in-itself. A closed set with no isolated point is called a perfect set.The number of isolated points is a topological invariant, i.e. if two topological spaces and are homeomorphic, the number of isolated points in each is equal.
  • Изоли́рованная то́чка в общей топологии — это такая точка множества, что пересечение некоторой её окрестности с множеством состоит только из этой точки.
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  • En topologie, un point x d'un espace topologique E est dit isolé si, intuitivement, il y a discontinuité en x (de tout côté) ; s'il n'a pas de voisin "collé" à lui.
  • Изоли́рованная то́чка в общей топологии — это такая точка множества, что пересечение некоторой её окрестности с множеством состоит только из этой точки.
  • In topology, a branch of mathematics concerning the study of shapes and spaces, a point x of a topological space X is called an isolated point of a subset S of X if x belongs to S and there exists in X a neighborhood of x not containing other points of S.
rdfs:label
  • Point isolé
  • Изолированная точка множества
  • Geïsoleerd punt
  • Isolated point
  • Isolierter Punkt
  • Punto aislado
  • Punto isolato
  • Изолирана точка
  • 孤立点
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