Orientability and Topology

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Orientability and Topology

Orientability vs. Topology

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. In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

Covering space and Orientability · Covering space and Topology · See more »

Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

Differentiable manifold and Orientability · Differentiable manifold and Topology · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

Euclidean space and Orientability · Euclidean space and Topology · See more »

Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

Homeomorphism and Orientability · Homeomorphism and Topology · See more »

Homology (mathematics)

In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.

Homology (mathematics) and Orientability · Homology (mathematics) and Topology · See more »

Homotopy

In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.

Homotopy and Orientability · Homotopy and Topology · See more »

Homotopy group

In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.

Homotopy group and Orientability · Homotopy group and Topology · See more »

Klein bottle

In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.

Klein bottle and Orientability · Klein bottle and Topology · See more »

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Manifold and Orientability · Manifold and Topology · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Mathematics and Orientability · Mathematics and Topology · See more »

Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

Orientability and Plane (geometry) · Plane (geometry) and Topology · See more »

Real projective plane

In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.

Orientability and Real projective plane · Real projective plane and Topology · See more »

Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

Orientability and Sphere · Sphere and Topology · See more »

Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

Orientability and Surface (topology) · Surface (topology) and Topology · See more »

Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Orientability and Torus · Topology and Torus · See more »