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

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....

{\displaystyle (x,o)} to x {\displaystyle x} is then a 2-to-1 covering map. This covering space is called the orientable double cover, as it is orientable...

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...

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...

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...

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...

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...

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...

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...

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...

(1)=x_{0}\right\}} which is the loop space Ω X {\displaystyle \Omega X} . See also: Path space fibration. Given a universal covering π : X ~ → X {\displaystyle...

mentioned above, the orbit space for this action is ⁠ R P n {\displaystyle \mathbb {RP} ^{n}} ⁠. This action is actually a covering space action giving ⁠ S n...

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...

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

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 −...

{\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...

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...

branched covering is a map that is almost a covering map, except on a small set. In topology, a map is a branched covering if it is a covering map everywhere...

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...

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

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...

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...

→ Z be the projection onto this invariant subspace. Then there is a covering space Cn corresponding to this projection map. Much like in the construction...

sequence of a fibration. For both the reals and complexes, SL is a covering space of PSL, with number of sheets equal to the number of nth roots in K;...

bi-monthly educational publication covering space tourism and space exploration developments in companies like SpaceX, Orbital Sciences, Virgin Galactic...

t^{-1}]/(x^{n}-t)} is etale and corresponds to a degree n {\displaystyle n} covering space of G m ∈ S c h / C {\displaystyle \mathbb {G} _{m}\in Sch/\mathbb {C}...

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...

^{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...

mathematics, the Vitali covering lemma is a combinatorial and geometric result commonly used in measure theory of Euclidean spaces. This lemma is an intermediate...