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essential supremum

Relationships observed in Wikidata. Connections do not establish verification or source support.

Release: sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Provider: Wikidata · graph projection only.

OBSERVED · GRAPH-PROJECTION · NOT ADMITTED · NOT VERIFIED · NOT SUPPORT

Edge identity is the provider property id (for example P31). It is not a Counterpedia predicate.

Development requests are not available on this deployment. The observed entity and its graph links remain readable.

Relationships of essential supremum

Show relationship types (drawing only; the text lists are unaffected)
studied by (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)different from (Observed provider relationships)part of (Observed provider relationships)studied by (Observed provider relationships)subclass of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)instance of (Observed provider relationships)subclass of (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)different from (Observed provider relationships)main subject (Observed provider relationships)Relationship label not yet available (Observed provider relationships)essential supremum — Wikidata entity (Q1969054)essentialsupremumWIKIDATA ENTITYfunctional analysis — Wikidata entity (Q190549)functionalanalysisWIKIDATA ENTITY\mathrm{ess } \sup f=\inf \{a \in \mathbb{R}: \mu(\{x: f(x) > a\}) = 0\} — Literal value (wikidata:literal:1:\mathrm{ess } \sup f=\inf \{a \in \mathbb{R}: \mu(\{x: f(x) > a\}) = 0\})\mathrm{ess }\sup f=\inf \{a…LITERAL VALUEWikiProject Mathematics — Wikidata entity (Q8487137)WikiProjectMathematicsWIKIDATA ENTITYsupremum — Wikidata entity (Q215071)supremumWIKIDATA ENTITYessential supremum and essential infimum — Wikidata entity (Q104804789)essentialsupremum and…WIKIDATA ENTITYmeasure theory — Wikidata entity (Q15614122)measure theoryWIKIDATA ENTITYelement — Wikidata entity (Q379825)elementWIKIDATA ENTITY\mathrm{ess}\sup — Literal value (wikidata:literal:7:\mathrm{ess}\sup)\mathrm{ess}\supLITERAL VALUEpartially ordered set — Wikidata entity (Q474715)partiallyordered setWIKIDATA ENTITYfunction — Wikidata entity (Q11348)functionWIKIDATA ENTITYquality — Wikidata entity (Q1207505)qualityWIKIDATA ENTITYess sup — Literal value (wikidata:literal:11:ess sup)ess supLITERAL VALUEessential infimum — Wikidata entity (Q20920008)essentialinfimumWIKIDATA ENTITY

Legend

  • Governed record relationships (solid)
  • Countergraph traversal (dashed)
  • Countergraph evidence (dotted)
  • Observed provider relationships (dash-dot)
  • Structurally derived (sparse dots)

Node shape identifies node kind only. Size, color, and position carry no meaning beyond hop distance from the root.

A line means a supported artifact carried an explicit structured relation. It does not mean the relation is true, admitted, verified, or authoritative.

Graph as text

Nodes (14)

  • essential supremum — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q1969054
    stable_ref
    Q1969054
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q1969054
    provider
    wikidata
    entity_href
    /entries/wikidata/Q1969054
  • functional analysis — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q190549
    stable_ref
    Q190549
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q190549
    provider
    wikidata
    entity_href
    /entries/wikidata/Q190549
  • \mathrm{ess } \sup f=\inf \{a \in \mathbb{R}: \mu(\{x: f(x) > a\}) = 0\} — Literal value
    Technical details
    node_id
    wikidata:literal:1:\mathrm{ess } \sup f=\inf \{a \in \mathbb{R}: \mu(\{x: f(x) > a\}) = 0\}
    stable_ref
    wikidata:literal:1:\mathrm{ess } \sup f=\inf \{a \in \mathbb{R}: \mu(\{x: f(x) > a\}) = 0\}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • WikiProject Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q8487137
    stable_ref
    Q8487137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q8487137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q8487137
  • supremum — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q215071
    stable_ref
    Q215071
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q215071
    provider
    wikidata
    entity_href
    /entries/wikidata/Q215071
  • essential supremum and essential infimum — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q104804789
    stable_ref
    Q104804789
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q104804789
    provider
    wikidata
    entity_href
    /entries/wikidata/Q104804789
  • measure theory — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q15614122
    stable_ref
    Q15614122
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q15614122
    provider
    wikidata
    entity_href
    /entries/wikidata/Q15614122
  • element — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q379825
    stable_ref
    Q379825
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q379825
    provider
    wikidata
    entity_href
    /entries/wikidata/Q379825
  • \mathrm{ess}\sup — Literal value
    Technical details
    node_id
    wikidata:literal:7:\mathrm{ess}\sup
    stable_ref
    wikidata:literal:7:\mathrm{ess}\sup
    node_kind
    wikidata_literal
    plane
    provider_observed
  • partially ordered set — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q474715
    stable_ref
    Q474715
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q474715
    provider
    wikidata
    entity_href
    /entries/wikidata/Q474715
  • function — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q11348
    stable_ref
    Q11348
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q11348
    provider
    wikidata
    entity_href
    /entries/wikidata/Q11348
  • quality — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q1207505
    stable_ref
    Q1207505
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q1207505
    provider
    wikidata
    entity_href
    /entries/wikidata/Q1207505
  • ess sup — Literal value
    Technical details
    node_id
    wikidata:literal:11:ess sup
    stable_ref
    wikidata:literal:11:ess sup
    node_kind
    wikidata_literal
    plane
    provider_observed
  • essential infimum — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q20920008
    stable_ref
    Q20920008
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q20920008
    provider
    wikidata
    entity_href
    /entries/wikidata/Q20920008

Edges (16)

  • essential supremum — studied by → functional analysis — Observed provider relationships
    Technical details
    machine_predicate
    P2579
    predicate_ref
    wikidata:property:P2579
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:0:P2579
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — Relationship label not yet available → \mathrm{ess } \sup f=\inf \{a \in \mathbb{R}: \mu(\{x: f(x) > a\}) = 0\} — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:1:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — Relationship label not yet available → WikiProject Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P6104
    predicate_ref
    wikidata:property:P6104
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:2:P6104
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — different from → supremum — Observed provider relationships
    Technical details
    machine_predicate
    P1889
    predicate_ref
    wikidata:property:P1889
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:3:P1889
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — part of → essential supremum and essential infimum — Observed provider relationships
    Technical details
    machine_predicate
    P361
    predicate_ref
    wikidata:property:P361
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:4:P361
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — studied by → measure theory — Observed provider relationships
    Technical details
    machine_predicate
    P2579
    predicate_ref
    wikidata:property:P2579
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:5:P2579
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — subclass of → element — Observed provider relationships
    Technical details
    machine_predicate
    P279
    predicate_ref
    wikidata:property:P279
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:6:P279
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — Relationship label not yet available → \mathrm{ess}\sup — Observed provider relationships
    Technical details
    machine_predicate
    P1993
    predicate_ref
    wikidata:property:P1993
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:7:P1993
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — Relationship label not yet available → partially ordered set — Observed provider relationships
    Technical details
    machine_predicate
    P13044
    predicate_ref
    wikidata:property:P13044
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:8:P13044
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — instance of → function — Observed provider relationships
    Technical details
    machine_predicate
    P31
    predicate_ref
    wikidata:property:P31
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:9:P31
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — subclass of → quality — Observed provider relationships
    Technical details
    machine_predicate
    P279
    predicate_ref
    wikidata:property:P279
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:10:P279
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — Relationship label not yet available → ess sup — Observed provider relationships
    Technical details
    machine_predicate
    P416
    predicate_ref
    wikidata:property:P416
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:11:P416
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum — Relationship label not yet available → essential infimum — Observed provider relationships
    Technical details
    machine_predicate
    P461
    predicate_ref
    wikidata:property:P461
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:12:P461
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • supremum — different from → essential supremum — Observed provider relationships
    Technical details
    machine_predicate
    P1889
    predicate_ref
    wikidata:property:P1889
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:13:P1889
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential supremum and essential infimum — main subject → essential supremum — Observed provider relationships
    Technical details
    machine_predicate
    P921
    predicate_ref
    wikidata:property:P921
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:14:P921
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • essential infimum — Relationship label not yet available → essential supremum — Observed provider relationships
    Technical details
    machine_predicate
    P461
    predicate_ref
    wikidata:property:P461
    provider
    wikidata
    provider_direction
    incoming
    plane
    provider_observed
    edge_id
    wikidata:relation:15:P461
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

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