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....

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...

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...

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...

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...

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...

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...

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...

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...

^{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...

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...

{\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...

{\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...

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...

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...

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...

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 −...

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...

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

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

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

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...

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...

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...

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

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