"upper semi-continuous" meaning in English

See upper semi-continuous in All languages combined, or Wiktionary

Adjective

Head templates: {{en-adj|-}} upper semi-continuous (not comparable)
  1. (of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at least that number is closed. Tags: not-comparable
    Sense id: en-upper_semi-continuous-en-adj-B6Td8m9X
  2. (of a real-valued function on a topological space) Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image. Tags: not-comparable Categories (topical): Mathematical analysis Synonyms: upper semicontinuous Related terms: lower semi-continuous Translations (Translations): unterhalbstetig (German)
    Sense id: en-upper_semi-continuous-en-adj-QvRUJ99k Disambiguation of Mathematical analysis: 11 89 Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms with non-redundant non-automated sortkeys Disambiguation of English entries with incorrect language header: 6 94 Disambiguation of English entries with topic categories using raw markup: 8 92 Disambiguation of English terms with non-redundant non-automated sortkeys: 12 88 Disambiguation of 'Translations': 6 94

Alternative forms

Download JSON data for upper semi-continuous meaning in English (2.5kB)

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "upper semi-continuous (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "glosses": [
        "Such that, for each fixed number, the subspace of points whose images are at least that number is closed."
      ],
      "id": "en-upper_semi-continuous-en-adj-B6Td8m9X",
      "links": [
        [
          "real-valued",
          "real-valued"
        ],
        [
          "function",
          "function"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "fixed",
          "fixed"
        ],
        [
          "number",
          "number"
        ],
        [
          "subspace",
          "subspace"
        ],
        [
          "point",
          "point"
        ],
        [
          "image",
          "image"
        ],
        [
          "at least",
          "at least"
        ],
        [
          "closed",
          "closed"
        ]
      ],
      "raw_glosses": [
        "(of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at least that number is closed."
      ],
      "raw_tags": [
        "of a real-valued function on a topological space"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "categories": [
        {
          "_dis": "6 94",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "8 92",
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "12 88",
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "11 89",
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image."
      ],
      "id": "en-upper_semi-continuous-en-adj-QvRUJ99k",
      "links": [
        [
          "neighborhood",
          "neighborhood"
        ],
        [
          "limit superior",
          "limit superior"
        ]
      ],
      "raw_glosses": [
        "(of a real-valued function on a topological space) Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image."
      ],
      "raw_tags": [
        "of a real-valued function on a topological space"
      ],
      "related": [
        {
          "_dis1": "30 70",
          "word": "lower semi-continuous"
        }
      ],
      "synonyms": [
        {
          "_dis1": "37 63",
          "word": "upper semicontinuous"
        }
      ],
      "tags": [
        "not-comparable"
      ],
      "translations": [
        {
          "_dis1": "6 94",
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "word": "unterhalbstetig"
        }
      ]
    }
  ],
  "word": "upper semi-continuous"
}
{
  "categories": [
    "English adjectives",
    "English entries with incorrect language header",
    "English entries with topic categories using raw markup",
    "English lemmas",
    "English multiword terms",
    "English terms with non-redundant non-automated sortkeys",
    "English uncomparable adjectives",
    "Translation table header lacks gloss",
    "en:Mathematical analysis"
  ],
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "upper semi-continuous (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "word": "lower semi-continuous"
    }
  ],
  "senses": [
    {
      "glosses": [
        "Such that, for each fixed number, the subspace of points whose images are at least that number is closed."
      ],
      "links": [
        [
          "real-valued",
          "real-valued"
        ],
        [
          "function",
          "function"
        ],
        [
          "topological space",
          "topological space"
        ],
        [
          "fixed",
          "fixed"
        ],
        [
          "number",
          "number"
        ],
        [
          "subspace",
          "subspace"
        ],
        [
          "point",
          "point"
        ],
        [
          "image",
          "image"
        ],
        [
          "at least",
          "at least"
        ],
        [
          "closed",
          "closed"
        ]
      ],
      "raw_glosses": [
        "(of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at least that number is closed."
      ],
      "raw_tags": [
        "of a real-valued function on a topological space"
      ],
      "tags": [
        "not-comparable"
      ]
    },
    {
      "glosses": [
        "Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image."
      ],
      "links": [
        [
          "neighborhood",
          "neighborhood"
        ],
        [
          "limit superior",
          "limit superior"
        ]
      ],
      "raw_glosses": [
        "(of a real-valued function on a topological space) Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image."
      ],
      "raw_tags": [
        "of a real-valued function on a topological space"
      ],
      "tags": [
        "not-comparable"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "upper semicontinuous"
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "word": "unterhalbstetig"
    }
  ],
  "word": "upper semi-continuous"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.