covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto...

Covering space, a map in the mathematical field of topology that locally looks like the projection of multiple copies of a space onto itself Covering...

opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping....

exhibits the portion y ≥ 1 of the upper half-plane as the universal covering space of the pseudosphere. The precise mapping is ( x , y ) ↦ ( v ( arcosh...

and the pia mater. Cerebrospinal fluid is located in the subarachnoid space between the arachnoid mater and the pia mater. The primary function of the...

example in topology is lifting a path in one topological space to a path in a covering space. For example, consider mapping opposite points on a sphere...

seen directly without using covering spaces. The group G is called the universal covering group of H. As the universal covering group suggests, there is...

Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically...

bundles include the Möbius strip and Klein bottle, as well as nontrivial covering spaces. Fiber bundles, such as the tangent bundle of a manifold and other...

mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is...

topology and the projection sending (x, o) to x is then a 2-to-1 covering map. This covering space is called the orientable double cover, as it is orientable...

{\displaystyle \chi (E)=\chi (F)\cdot \chi (B).} This includes product spaces and covering spaces as special cases, and can be proven by the Serre spectral sequence...

In mathematics, and more particularly in set theory, a cover (or covering) of a set X {\displaystyle X} is a family of subsets of X {\displaystyle X} whose...

action on Sn. As mentioned above, the orbit space for this action is RPn. This action is actually a covering space action giving Sn as a double cover of RPn...

connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally simply connected if there is a...

In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or...

^{1}} which ramifies at three points. Then, there is an associated covering space C | U → U = P 1 − { p 1 , p 2 , p 3 } {\displaystyle C|_{U}\to U=\mathbb...

but examples of covering spaces of topological spaces, so the terminology in the theory of covering spaces is available; say covering transformation group...

lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a topological space E to another one, B. It is...

several loosely related functors that generalise the functors taking a covering space π : X → S {\displaystyle \pi \colon X\rightarrow S} to the fiber π −...

Euler characteristic of a space and a ramified cover. For example, hyperbolic Riemann surfaces are ramified covering spaces of the sphere (they have non-constant...

connected based topological space with base point x, and let p : X ~ → X {\displaystyle p:{\tilde {X}}\to X} be a covering with fiber F = p − 1 ( x ) {\displaystyle...

system (2018). A coordinate patch covering part of the space gives the half-space coordinatization of anti-de Sitter space. The metric tensor for this patch...

In mathematics, a covering number is the number of balls of a given size needed to completely cover a given space, with possible overlaps between the...

every subgroup G of π1(X), there is a covering space with G as its fundamental group. Given an inner product space V, we can form the orthogonal complement...

original space; space-filling curves provide such examples. Topology Covering space – Type of continuous map in topology Disjoint union (topology) – space formed...

graph X. The main theorem on covering spaces tells us that every subgroup H of G is the fundamental group of some covering space Y of X; but every such Y...

universal covering space, though not all authors include the assumption on the homotopy type. For example, any topological group is a simple space (provided...

simply-connected hyperbolic space form is homothetic to hyperbolic space. Using the covering manifold construction, any Riemannian space form is isometric to...

Lie groups by discrete groups are the same as covering groups. More precisely, a connected covering space G∗ of a connected Lie group G is naturally a...