Heine–Borel theorem

theorem about compact sets in Euclidean space
Intangible theorem Q253214
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Heine–Borel theorem

Summary

Heine–Borel theorem is a theorem[1]. It ranks in the top 8% of theorem entities by monthly Wikipedia readership (135 views/month).[2]

Key Facts

  • Heine–Borel theorem's instance of is recorded as theorem[3].
  • Eduard Heine is named after Heine–Borel theorem[4].
  • Émile Borel is named after Heine–Borel theorem[5].
  • Henri Lebesgue is named after Heine–Borel theorem[6].
  • Heine–Borel theorem is part of list of theorems[7].
  • Heine–Borel theorem's studied by is recorded as calculus[8].
  • Heine–Borel theorem's maintained by WikiProject is recorded as WikiProject Mathematics[9].

Body

Definition and Type

Heine–Borel theorem's instance of is recorded as theorem[3].

Origins

Things named after include Eduard Heine[4], a mathematician[10], 1821–1881[11], of Kingdom of Prussia[12], awarded the Carl Friedrich Gauss Medal[13], specialised in mathematical analysis[14]; Émile Borel[5], a mathematician[15], 1871–1956[16], of France[17], awarded the Grand Cross of the Legion of Honour[18], specialised in probability theory[19]; and Henri Lebesgue[6], a mathematician[20], 1875–1941[21], of France[22], awarded the Poncelet Prize[23], specialised in mathematical analysis[24].

Use and Application

Heine–Borel theorem is part of list of theorems[7].

Why It Matters

Heine–Borel theorem ranks in the top 8% of theorem entities by monthly Wikipedia readership (135 views/month).[2] It has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[25] It is known by 16 alternative names across languages and contexts.[26]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.

Inline context (facts about related entities)

  1. [10] . Wikidata. wikidata.org. → on this site
  2. [11] . Wikidata. wikidata.org. → on this site
  3. [12] . Wikidata. wikidata.org. → on this site
  4. [13] . Wikidata. wikidata.org. → on this site
  5. [14] . Wikidata. wikidata.org. → on this site
  6. [15] . Wikidata. wikidata.org. → on this site
  7. [16] . Wikidata. wikidata.org. → on this site
  8. [17] . Wikidata. wikidata.org. → on this site
  9. [18] . Wikidata. wikidata.org. → on this site
  10. [19] . Wikidata. wikidata.org. → on this site
  11. [20] . Wikidata. wikidata.org. → on this site
  12. [21] . Wikidata. wikidata.org. → on this site
  13. [22] . Wikidata. wikidata.org. → on this site
  14. [23] . Wikidata. wikidata.org. → on this site
  15. [24] . Wikidata. wikidata.org. → on this site

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [25] . Wikidata sitelinks. wikidata.org.
  3. [26] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Heine–Borel theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/heine-borel-theorem
MLA “Heine–Borel theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/heine-borel-theorem.
BibTeX @misc{4ortxyz_heine-borel-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Heine–Borel theorem}}, year = {2026}, url = {https://4ort.xyz/entity/heine-borel-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Heine–Borel theorem — https://4ort.xyz/entity/heine-borel-theorem (retrieved 2026-05-03)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 16d ago · Mynus grey · 2026-07-02 view diff on Wikidata ↗
    P14534 Metric.isCompact_iff_isClosed_bounded
    "/* wbcreateclaim-create:1| */ [[Property:P14534]]: Metric.isCompact_iff_isClosed_bounded, #quickstatements; #temporary_batch_1783013068346"
  2. 11w ago · נדב ס · 2026-04-30 view diff on Wikidata ↗
    Named after
    Part of list of theorems
    Instance of
    Studied by calculus
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-update:2||1 */ [[Property:P2534]]: C_T = C_K \cup \{U\}"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.