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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....

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...

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...

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...

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...

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...

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...

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...

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...

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...

^{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...

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...

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...