"Baire space" meaning in English

{
  "etymology_text": "Introduced by René-Louis Baire.",
  "forms": [
    {
      "form": "Baire spaces",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Baire space (plural Baire spaces)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A topological space such that every intersection of a countable collection of open dense sets in the space is also dense."
      ],
      "id": "en-Baire_space-en-noun-OnNJJVar",
      "links": [
        [
          "topological space",
          "topological space"
        ],
        [
          "intersection",
          "intersection"
        ],
        [
          "countable",
          "countable"
        ],
        [
          "collection",
          "collection"
        ],
        [
          "open",
          "open"
        ],
        [
          "dense",
          "dense"
        ],
        [
          "set",
          "set"
        ]
      ],
      "wikipedia": [
        "Baire space"
      ]
    }
  ],
  "word": "Baire space"
}

{
  "etymology_text": "Introduced by René-Louis Baire.",
  "forms": [
    {
      "form": "Baire spaces",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Baire space (plural Baire spaces)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "en:Topology"
      ],
      "glosses": [
        "A topological space such that every intersection of a countable collection of open dense sets in the space is also dense."
      ],
      "links": [
        [
          "topological space",
          "topological space"
        ],
        [
          "intersection",
          "intersection"
        ],
        [
          "countable",
          "countable"
        ],
        [
          "collection",
          "collection"
        ],
        [
          "open",
          "open"
        ],
        [
          "dense",
          "dense"
        ],
        [
          "set",
          "set"
        ]
      ],
      "wikipedia": [
        "Baire space"
      ]
    }
  ],
  "word": "Baire space"
}