space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map. Intuitively, a contractible space is...

theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e., a topological space all of whose homotopy...

infinite-dimensional case of separable Hilbert space, basically because the space of upper triangular matrices is contractible as can be seen quite explicitly. The...

to the circle or to the higher spheres is null-homotopic. If a space X is contractible, then it is also acyclic, by the homotopy invariance of homology...

{\displaystyle \mathbb {R} _{M}} on M. The singular cohomology of a contractible space vanishes in positive degree, but the Poincaré lemma does not follow...

notion of a contractible space. Every contractible space is path connected and thus also connected. In general, any path connected space must be connected...

Space Exploration Technologies Corporation, commonly referred to as SpaceX, is an American spacecraft manufacturer, launch service provider and satellite...

this space is weakly contractible. Since S ∞ {\displaystyle S^{\infty }} is moreover a CW-complex, it is also contractible. See Contractibility of unit...

its quotient spaces. A quotient space of a simply connected or contractible space need not share those properties. Compactness If a space is compact, then...

never occur in a spacetime which is homeomorphic to Rn, which is a contractible space. However, for Kaluza–Klein theories, the Scherk–Schwarz mechanism...

space:" Space Superiority (in space) Global Mission Operations (from space) Assured Space Access (to space) Space superiority defends against space and...

conjecture was disproved by Kinoshita who found an example of a compact contractible space without the FPP. In domain theory, the notion and terminology of fixed...

prove: Proposition. Let G be a compact Lie group. There exists a contractible space EG on which G acts freely. The projection EG → BG is a G-principal...

business unit of SpaceX for the creation of purpose-built low-Earth-orbit satellites designed to provide new "disruptive" military space capabilities to...

embeds a space as a subspace of a contractible space. When X is compact and Hausdorff (essentially, when X can be embedded in Euclidean space), then the...

but it is not a contractible space. An n-cell is a space homeomorphic to the closed ball in the Euclidean space Rn. It is contractible and is the simplest...

is an n-dimensional vector space. For n = 1, one has EU(1) = S∞, which is known to be a contractible space. The base space is then BU(1) = CP∞, the infinite-dimensional...

space agencies and private spaceflight companies. This collaboration is bound together by the Artemis Accords and governmental contracts. The Space Launch...

that deformation retracts to a point is contractible and vice versa. However, there exist contractible spaces that do not strongly deformation retract...

any contractible space – has a trivial fundamental group. Thus, the fundamental group does not distinguish between such spaces. A path-connected space whose...

is open. Continuum A space is called a continuum if it a compact, connected Hausdorff space. Contractible A space X is contractible if the identity map...

universal space X ^ {\displaystyle {\widehat {X}}} through which any map of X to a nilpotent space N factors uniquely up to a contractible space of choices...

could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable...

Raptor is a family of rocket engines developed and manufactured by SpaceX. A notable trait of this engine family is the use of a full-flow staged combustion...

being locally contractible. A strictly weaker condition is that of being semi-locally simply connected. Both locally simply connected spaces and simply connected...

developed, manufactured, and operated by American space company SpaceX, for flights to the International Space Station (ISS) and private spaceflight missions...

Euler characteristic is also a homotopy invariant. For example, any contractible space (that is, one homotopy equivalent to a point) has trivial homology...

point. This means that U(H) is weakly contractible, and an additional argument shows that it is actually contractible. Note that this is a purely infinite...

A contractible manifold is one that can continuously be shrunk to a point inside the manifold itself. For example, an open ball is a contractible manifold...

Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions...