# Classifier Instance:

Anchor text: Riemannian manifold
Target Entity: Riemannian_manifold
Preceding Context: In modern mathematics, Euclidean spaces form the prototypes for other, more complicated geometric objects. For example, a smooth manifold is a Hausdorff topological space that is locally diffeomorphic to Euclidean space. Diffeomorphism does not respect distance and angle, so these key concepts of Euclidean geometry are lost on a smooth manifold. However, if one additionally prescribes a smoothly varying inner product on the manifold's tangent spaces, then the result is what is called a
Succeeding Context: . Put differently, a Riemannian manifold is a space constructed by deforming and patching together Euclidean spaces. Such a space enjoys notions of distance and angle, but they behave in a curved, non-Euclidean manner. The simplest Riemannian manifold, consisting of R n with a constant inner product, is essentially identical to Euclidean n-space itself.
Paragraph Title: Generalizations
Source Page: Euclidean space

## Ground Truth Types:

|---wordnet_entity_100001740
|  |---wordnet_artifact_100021939
|  |  |---wordnet_structure_104341686
|  |  |  |---wordnet_structure_104341686_rest
|  |---yagoGeoEntity
|  |  |---wordnet_structure_104341686
|  |  |  |---wordnet_structure_104341686_rest

## Predicted Types:

TypeConfidenceDecision
wordnet_artifact_1000219391.1583032801243638 1
wordnet_instrumentality_103575240-1.6737897118567187 0
wordnet_structure_1043416860.8410534185010371 1
wordnet_building_102913152-1.8672857600425723 0
wordnet_memorial_103743902-1.226783767533697 0
wordnet_housing_103546340-1.1715422090916543 0
wordnet_building_complex_102914991-1.019928448484098 0
wordnet_establishment_103297735-1.2762511783824544 0
wordnet_obstruction_103839993-1.211559402609971 0
wordnet_area_102735688-1.430011483741307 0
wordnet_tower_104460130-1.384316298076072 0
wordnet_bridge_102898711-1.2173305761194093 0
wordnet_facility_103315023-2.6389646796448316 0
wordnet_creation_103129123-2.4352023108417957 0
wordnet_article_100022903-1.5325601496385666 0
wordnet_commodity_103076708-1.5879510630314848 0
wordnet_way_104564698-1.4101547591009944 0
wordnet_covering_103122748-1.5787427661025837 0
wordnet_event_100029378-1.9241727068602652 0
wordnet_organization_108008335-2.6692104417136546 0
wordnet_person_100007846-2.0750517598274087 0
yagoGeoEntity0.7567526645699689 1
wordnet_location_100027167-1.8087454774350769 0
wordnet_structure_1043416861.2003179759386737 1
wordnet_building_102913152-1.8672857600425723 0
wordnet_memorial_103743902-1.226783767533697 0
wordnet_housing_103546340-1.1715422090916543 0
wordnet_building_complex_102914991-1.019928448484098 0
wordnet_establishment_103297735-1.2762511783824544 0
wordnet_obstruction_103839993-1.211559402609971 0
wordnet_area_102735688-1.430011483741307 0
wordnet_tower_104460130-1.384316298076072 0
wordnet_bridge_102898711-1.2173305761194093 0
wordnet_facility_103315023-2.2061982138371268 0
wordnet_body_of_water_109225146-1.761489348931526 0
wordnet_geological_formation_109287968-1.5837641820754311 0
wordnet_way_104564698-1.3176725754309961 0
wordnet_land_109334396-1.6135645021685814 0
|---wordnet_entity_100001740
|  |---wordnet_artifact_100021939
|  |  |---wordnet_instrumentality_103575240
|  |  |---wordnet_structure_104341686
|  |  |  |---wordnet_building_102913152
|  |  |  |---wordnet_memorial_103743902
|  |  |  |---wordnet_housing_103546340
|  |  |  |---wordnet_building_complex_102914991
|  |  |  |---wordnet_establishment_103297735
|  |  |  |---wordnet_stadium_104295881
|  |  |  |---wordnet_obstruction_103839993
|  |  |  |---wordnet_area_102735688
|  |  |  |---wordnet_tower_104460130
|  |  |  |---wordnet_bridge_102898711
|  |  |---wordnet_facility_103315023
|  |  |---wordnet_creation_103129123
|  |  |---wordnet_article_100022903
|  |  |---wordnet_commodity_103076708
|  |  |---wordnet_way_104564698
|  |  |---wordnet_covering_103122748
|  |---wordnet_event_100029378
|  |---wordnet_organization_108008335
|  |---wordnet_person_100007846
|  |---yagoGeoEntity
|  |  |---wordnet_location_100027167
|  |  |---wordnet_structure_104341686
|  |  |  |---wordnet_building_102913152
|  |  |  |---wordnet_memorial_103743902
|  |  |  |---wordnet_housing_103546340
|  |  |  |---wordnet_building_complex_102914991
|  |  |  |---wordnet_establishment_103297735
|  |  |  |---wordnet_stadium_104295881
|  |  |  |---wordnet_obstruction_103839993
|  |  |  |---wordnet_area_102735688
|  |  |  |---wordnet_tower_104460130
|  |  |  |---wordnet_bridge_102898711
|  |  |---wordnet_facility_103315023
|  |  |---wordnet_body_of_water_109225146
|  |  |---wordnet_geological_formation_109287968
|  |  |---wordnet_way_104564698
|  |  |---wordnet_land_109334396