"accumulation point" meaning in Anglais

{
  "antonyms": [
    {
      "word": "isolated point"
    }
  ],
  "categories": [
    {
      "kind": "other",
      "name": "Locutions nominales en anglais",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "Anglais",
      "orig": "anglais",
      "parents": [],
      "source": "w"
    }
  ],
  "derived": [
    {
      "word": "complete accumulation point"
    }
  ],
  "forms": [
    {
      "form": "accumulation points",
      "tags": [
        "plural"
      ]
    }
  ],
  "hypernyms": [
    {
      "word": "limit point"
    }
  ],
  "lang": "Anglais",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "Locution nominale",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "Exemples en anglais",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Exemples en anglais à traduire",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Lexique en anglais de la topologie",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              76,
              94
            ]
          ],
          "ref": "Bert Mendelson, Introduction to Topology, Dover Publications, Inc., New York, 1990, 3ᵉ édition (1ʳᵉ édition 1975), page 173, ISBN 0-486-66352-3 (OCLC 932232056), § 5.3",
          "text": "LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a∈X is an accumulation point of A if and only if a is a limit point of A."
        },
        {
          "text": "{{exemple|A set A has an accumulation pointp if for every ϵ>0 there is an x∈A with x ne p and |x-p|<ϵ. Informally, p is an accumulation point of A if there are points of A that are arbitrarily close to p. Note that the fact that p is an accumulation point of the set A has nothing to do with whether p is actually an element of A. For example, the set A=n∈ℕ} has one accumulation point, 0, because for every ϵ>0 there is an n∈ℕ with 1/n<ϵ. Here the accumulation point 0 is not an element of the set A."
        }
      ],
      "glosses": [
        "Point d’accumulation."
      ],
      "id": "fr-accumulation_point-en-noun-G9NBOIP1",
      "topics": [
        "topology"
      ]
    },
    {
      "categories": [
        {
          "kind": "other",
          "name": "Exemples en anglais",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Exemples en anglais à traduire",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              71,
              89
            ],
            [
              253,
              271
            ],
            [
              385,
              403
            ]
          ],
          "ref": "Milos Marek, Igor Schreiber, Chaotic Behaviour of Deterministic Dissipative Systems, Cambridge University Press, 1995, page 77",
          "text": "The chaotic set (not necessarily attracting) is formed after the first accumulation point (a_∞≈3.570 for the logistic mapping) is reached. In the chaotic region of the logistic map the periodicity re-emerges in periodic windows which are bounded by the accumulation point from the right and by the saddle-node bifurcation from the left. A reverse bifurcation sequence occurs above the accumulation point."
        }
      ],
      "glosses": [
        "Point au-delà duquel les orbites périodiques deviennent chaotiques."
      ],
      "id": "fr-accumulation_point-en-noun--6GLJfTW",
      "raw_tags": [
        "Dynamique des systèmes"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "cluster point"
    }
  ],
  "word": "accumulation point"
}

{
  "antonyms": [
    {
      "word": "isolated point"
    }
  ],
  "categories": [
    "Locutions nominales en anglais",
    "anglais"
  ],
  "derived": [
    {
      "word": "complete accumulation point"
    }
  ],
  "forms": [
    {
      "form": "accumulation points",
      "tags": [
        "plural"
      ]
    }
  ],
  "hypernyms": [
    {
      "word": "limit point"
    }
  ],
  "lang": "Anglais",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "Locution nominale",
  "senses": [
    {
      "categories": [
        "Exemples en anglais",
        "Exemples en anglais à traduire",
        "Lexique en anglais de la topologie"
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              76,
              94
            ]
          ],
          "ref": "Bert Mendelson, Introduction to Topology, Dover Publications, Inc., New York, 1990, 3ᵉ édition (1ʳᵉ édition 1975), page 173, ISBN 0-486-66352-3 (OCLC 932232056), § 5.3",
          "text": "LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a∈X is an accumulation point of A if and only if a is a limit point of A."
        },
        {
          "text": "{{exemple|A set A has an accumulation pointp if for every ϵ>0 there is an x∈A with x ne p and |x-p|<ϵ. Informally, p is an accumulation point of A if there are points of A that are arbitrarily close to p. Note that the fact that p is an accumulation point of the set A has nothing to do with whether p is actually an element of A. For example, the set A=n∈ℕ} has one accumulation point, 0, because for every ϵ>0 there is an n∈ℕ with 1/n<ϵ. Here the accumulation point 0 is not an element of the set A."
        }
      ],
      "glosses": [
        "Point d’accumulation."
      ],
      "topics": [
        "topology"
      ]
    },
    {
      "categories": [
        "Exemples en anglais",
        "Exemples en anglais à traduire"
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              71,
              89
            ],
            [
              253,
              271
            ],
            [
              385,
              403
            ]
          ],
          "ref": "Milos Marek, Igor Schreiber, Chaotic Behaviour of Deterministic Dissipative Systems, Cambridge University Press, 1995, page 77",
          "text": "The chaotic set (not necessarily attracting) is formed after the first accumulation point (a_∞≈3.570 for the logistic mapping) is reached. In the chaotic region of the logistic map the periodicity re-emerges in periodic windows which are bounded by the accumulation point from the right and by the saddle-node bifurcation from the left. A reverse bifurcation sequence occurs above the accumulation point."
        }
      ],
      "glosses": [
        "Point au-delà duquel les orbites périodiques deviennent chaotiques."
      ],
      "raw_tags": [
        "Dynamique des systèmes"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "cluster point"
    }
  ],
  "word": "accumulation point"
}