"accumulation point" meaning in English

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      "form": "accumulation points",
      "tags": [
        "plural"
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  "lang_code": "en",
  "pos": "noun",
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          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
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          "langcode": "en",
          "name": "Systems theory",
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          "name": "Topology",
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      "examples": [
        {
          "ref": "1975, Bert Mendelson, Introduction to Topology, 3rd edition, New York: Dover Publications, Inc., published 1990, →ISBN, →OCLC, §5.3, page 173:",
          "text": "LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a#x5C;inX is an accumulation point of A if and only if a is a limit point of A.",
          "type": "quote"
        },
        {
          "text": "2008, Brian S. Thomson, Andrew M. Bruckner, Judith B. Bruckner, Elementary Real Analysis, Volume 1, Thomson-Bruckner (ClassicalRealAnalysis.com), 2nd Edition, page 153,\nDefinition 4.9 (Closed): The set E is said to be closed provided that every accumulation point of E belongs to the set E.\nThus a set E is not closed if there is some accumulation point of E that does not belong to E. In particular, a set with no accumulation points would have to be closed since there is no point that needs to be checked."
        },
        {
          "text": "{{quote-book|en|year=2016|author=Jonathan M. Kane|title=Writing Proofs in Analysis|pageurl=https://books.google.com.au/books?id=Hm1BDAAAQBAJ&pg=PA74&dq=%22accumulation+point%22%7C%22accumulation+points%22&hl=en&sa=X&ved=2ahUKEwjXmIa0qoPrAhVWWysKHSMKDhAQ6AEwAnoECAYQAg#v=onepage&q=%22accumulation%20point%22%7C%22accumulation%20points%22&f=false|page=74|publisher=Springer"
        }
      ],
      "glosses": [
        "Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S."
      ],
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      "qualifier": "\"of\" a subset of a topological space",
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        "(topology, \"of\" a subset of a topological space) Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S."
      ],
      "synonyms": [
        {
          "word": "cluster point"
        },
        {
          "word": "limit point"
        }
      ],
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      "wikipedia": [
        "Encyclopedia of Mathematics",
        "MathWorld"
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  "word": "accumulation point"
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{
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    {
      "form": "accumulation points",
      "tags": [
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      "expansion": "accumulation point (plural accumulation points)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        "en:Mathematical analysis",
        "en:Systems theory",
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          "ref": "1975, Bert Mendelson, Introduction to Topology, 3rd edition, New York: Dover Publications, Inc., published 1990, →ISBN, →OCLC, §5.3, page 173:",
          "text": "LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a#x5C;inX is an accumulation point of A if and only if a is a limit point of A.",
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        },
        {
          "text": "2008, Brian S. Thomson, Andrew M. Bruckner, Judith B. Bruckner, Elementary Real Analysis, Volume 1, Thomson-Bruckner (ClassicalRealAnalysis.com), 2nd Edition, page 153,\nDefinition 4.9 (Closed): The set E is said to be closed provided that every accumulation point of E belongs to the set E.\nThus a set E is not closed if there is some accumulation point of E that does not belong to E. In particular, a set with no accumulation points would have to be closed since there is no point that needs to be checked."
        },
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          "text": "{{quote-book|en|year=2016|author=Jonathan M. Kane|title=Writing Proofs in Analysis|pageurl=https://books.google.com.au/books?id=Hm1BDAAAQBAJ&pg=PA74&dq=%22accumulation+point%22%7C%22accumulation+points%22&hl=en&sa=X&ved=2ahUKEwjXmIa0qoPrAhVWWysKHSMKDhAQ6AEwAnoECAYQAg#v=onepage&q=%22accumulation%20point%22%7C%22accumulation%20points%22&f=false|page=74|publisher=Springer"
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        "Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S."
      ],
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        "(topology, \"of\" a subset of a topological space) Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S."
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          "word": "cluster point"
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        {
          "word": "limit point"
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  "word": "accumulation point"
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