Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Orientability> ?p ?o }
- Orientability abstract "In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the surface, as needed by Stokes' theorem for instance. More generally, orientability of an abstract surface, or manifold, measures whether one can consistently choose a "clockwise" orientation for all loops in the manifold. Equivalently, a surface is orientable if a two-dimensional figure such as 20px in the space cannot be moved (continuously) around the space and back to where it started so that it looks like its own mirror image 20px.The notion of orientability can be generalised to higher-dimensional manifolds as well. A manifold is orientable if it has a consistent choice of orientation, and a connected orientable manifold has exactly two different possible orientations. In this setting, various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. An important generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.".
- Orientability thumbnail Torus.png?width=300.
- Orientability wikiPageExternalLink Orientation.
- Orientability wikiPageExternalLink Orientation_covering.
- Orientability wikiPageExternalLink Orientation_of_manifolds.
- Orientability wikiPageExternalLink Orientation_of_manifolds_in_generalized_cohomology_theories.
- Orientability wikiPageID "187446".
- Orientability wikiPageLength "16834".
- Orientability wikiPageOutDegree "81".
- Orientability wikiPageRevisionID "671460357".
- Orientability wikiPageWikiLink 3-manifold.
- Orientability wikiPageWikiLink Alternating_group.
- Orientability wikiPageWikiLink Associated_bundle.
- Orientability wikiPageWikiLink Atlas_(topology).
- Orientability wikiPageWikiLink Category:Articles_containing_video_clips.
- Orientability wikiPageWikiLink Category:Differential_topology.
- Orientability wikiPageWikiLink Category:Surfaces.
- Orientability wikiPageWikiLink Causal_structure.
- Orientability wikiPageWikiLink Character_theory.
- Orientability wikiPageWikiLink Connected_component_(topology).
- Orientability wikiPageWikiLink Connected_space.
- Orientability wikiPageWikiLink Coordinate_atlas.
- Orientability wikiPageWikiLink Covering_space.
- Orientability wikiPageWikiLink Curve_orientation.
- Orientability wikiPageWikiLink Determinant.
- Orientability wikiPageWikiLink Differentiable_manifold.
- Orientability wikiPageWikiLink Differentiable_manifolds.
- Orientability wikiPageWikiLink Differential_form.
- Orientability wikiPageWikiLink Euclidean_space.
- Orientability wikiPageWikiLink Even_and_odd_permutations.
- Orientability wikiPageWikiLink Fiber_bundle.
- Orientability wikiPageWikiLink Frame_bundle.
- Orientability wikiPageWikiLink GL(n).
- Orientability wikiPageWikiLink General_linear_group.
- Orientability wikiPageWikiLink General_relativity.
- Orientability wikiPageWikiLink Homeomorphic.
- Orientability wikiPageWikiLink Homeomorphism.
- Orientability wikiPageWikiLink Homology_(mathematics).
- Orientability wikiPageWikiLink Homology_theory.
- Orientability wikiPageWikiLink Homotopy.
- Orientability wikiPageWikiLink Homotopy_equivalence.
- Orientability wikiPageWikiLink Homotopy_group.
- Orientability wikiPageWikiLink Immersion_(mathematics).
- Orientability wikiPageWikiLink Index_of_a_subgroup.
- Orientability wikiPageWikiLink Jacobian_determinant.
- Orientability wikiPageWikiLink Jacobian_matrix_and_determinant.
- Orientability wikiPageWikiLink Klein_bottle.
- Orientability wikiPageWikiLink Lorentzian_manifold.
- Orientability wikiPageWikiLink Manifold.
- Orientability wikiPageWikiLink Mathematics.
- Orientability wikiPageWikiLink Matrix_(mathematics).
- Orientability wikiPageWikiLink Möbius_strip.
- Orientability wikiPageWikiLink Normal_(geometry).
- Orientability wikiPageWikiLink Orientation_(mathematics).
- Orientability wikiPageWikiLink Orientation_(vector_space).
- Orientability wikiPageWikiLink Parity_of_a_permutation.
- Orientability wikiPageWikiLink Plane_(geometry).
- Orientability wikiPageWikiLink Plane_(mathematics).
- Orientability wikiPageWikiLink Pseudo-Riemannian_manifold.
- Orientability wikiPageWikiLink Real_projective_plane.
- Orientability wikiPageWikiLink Reduction_of_the_structure_group.
- Orientability wikiPageWikiLink Relative_homology.
- Orientability wikiPageWikiLink Right-hand_rule.
- Orientability wikiPageWikiLink Section_(fiber_bundle).
- Orientability wikiPageWikiLink Singular_homology.
- Orientability wikiPageWikiLink Smooth_function.
- Orientability wikiPageWikiLink Smoothness.
- Orientability wikiPageWikiLink Solid_Klein_bottle.
- Orientability wikiPageWikiLink Space-time.
- Orientability wikiPageWikiLink Spacetime.
- Orientability wikiPageWikiLink Sphere.
- Orientability wikiPageWikiLink Stokes_theorem.
- Orientability wikiPageWikiLink Structure_group.
- Orientability wikiPageWikiLink Surface.
- Orientability wikiPageWikiLink Surface_normal.
- Orientability wikiPageWikiLink Symmetric_group.
- Orientability wikiPageWikiLink Tangent_bundle.
- Orientability wikiPageWikiLink Torus.
- Orientability wikiPageWikiLink Triangulation_(topology).
- Orientability wikiPageWikiLink Vector_bundle.
- Orientability wikiPageWikiLink Volume_form.
- Orientability wikiPageWikiLink File:MobiusStrip-01.png.
- Orientability wikiPageWikiLink File:Orientation_cover_of_Mobius_strip.webm.
- Orientability wikiPageWikiLink File:Pie_2.svg.
- Orientability wikiPageWikiLink File:Small_pie.svg.
- Orientability wikiPageWikiLink File:Steiners_Roman_Surface.gif.
- Orientability wikiPageWikiLink File:Surface_orientation.gif.
- Orientability wikiPageWikiLink File:Torus.png.
- Orientability wikiPageWikiLinkText "''oriented'' manifolds".
- Orientability wikiPageWikiLinkText "Non-orientable".
- Orientability wikiPageWikiLinkText "Orientability".
- Orientability wikiPageWikiLinkText "Orientability#Orientability of manifolds".
- Orientability wikiPageWikiLinkText "Orientability#Orientable double cover".
- Orientability wikiPageWikiLinkText "lack of orientation".
- Orientability wikiPageWikiLinkText "non-orientable surfaces".
- Orientability wikiPageWikiLinkText "non-orientable".
- Orientability wikiPageWikiLinkText "nonorientability".
- Orientability wikiPageWikiLinkText "orientability".
- Orientability wikiPageWikiLinkText "orientable and non-orientable surfaces".
- Orientability wikiPageWikiLinkText "orientable double cover".