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In topology, a branch of mathematics, a topological space X is said to be simply connected at infinity if for any compact subset C of X, there is a compact set D in X containing C so that the induced map
is the zero map. Intuitively, this is the property that loops far away from a small subspace of X can be collapsed, no matter how bad the small subspace is.
The Whitehead manifold is an example of a 3-manifold that is contractible but not simply connected at infinity. Since this property is invariant under homeomorphism, this proves that the Whitehead manifold is not homeomorphic to R3.
However, it is a theorem of John R. Stallings[1] that for , a contractible n-manifold is homeomorphic to Rn precisely when it is simply connected at infinity.
a branch of mathematics, a topological space X is said to be simplyconnectedatinfinity if for any compact subset C of X, there is a compact set D in...
{\displaystyle \mathbb {R} ^{3}.} The reason is that it is not simplyconnectedatinfinity. The one point compactification of X is the space S 3 / W {\displaystyle...
M. Mihalik implies that F is simplyconnectedatinfinity, and the stated result implies that all homology atinfinity vanishes, the claim about homotopy...
conditions are path connected, simplyconnected, and n {\displaystyle n} -connected. Another related notion is locally connected, which neither implies nor...
hosohedron atinfinity, composed of an infinite number of digons meeting at two antipodal points atinfinity. However, as the vertices of these digons are at infinity...
published by Activision, starting in 2003. The games were first developed by Infinity Ward, then by Treyarch and Sledgehammer Games. Several spin-off and handheld...
Thanos: The Infinity Relativity, was released in June, 2015. The third graphic novel, Thanos: The Infinity Finale, as well as the connected mini-series...
In mathematics, hyperbolic space of dimension n is the unique simplyconnected, n-dimensional Riemannian manifold of constant sectional curvature equal...
+ c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0} , i.e., for which the sequence f...
appeared in the graphic novel Thanos: The Infinity Finale as well as in the connected mini-series The Infinity Entity (both published in 2016), also written...
conformal homeomorphism of the sphere at infinity (and conversely, every conformal homeomorphism on the sphere atinfinity extends uniquely to a hyperbolic isometry...
simplyconnected set D, which can be considered as the inverse of the conformal radius of the complement E = Dc viewed from infinity. Given a simply connected...
every closed differential 1-form of compact support is exact. Every simplyconnected Riemann surface is planar. The class of planar Riemann surfaces was...
its proof. The statement is as follows: Let U {\displaystyle U} be a simplyconnected open subset of the complex plane containing a finite list of points...
the Infinity Stones akin to the Infinity Gauntlet and created to reverse the Blip. After the Avengers retrieve alternate versions of the six Infinity Stones...
does not, then the value of the function will approach infinity; if both parts have a zero at z, then one must compare the multiplicity of these zeros...
entire and has an essential singularity atinfinity, so not defined atinfinity, and misses zero and infinity), but all maps from zero punctures to one...
special interest like singular points, inflection points and points atinfinity. More advanced questions involve the topology of the curve and the relationship...
mathematical infinity appears in the Yajur Veda, an ancient Indian script, which at one point states, "If you remove a part from infinity or add a part...
and connectedness.[citation needed] Rogue Moon Anatta, the Buddhist doctrine of the non-existence of the self "Heaven Sent" (Doctor Who) Infinity Pool...
relationship between the infinity of God and mathematical infinity has often been discussed. Georg Cantor's work on infinity in mathematics was accused...
= 1 {\textstyle z_{1}=1} . Because C {\textstyle \mathbb {C} } is simplyconnected and the range of f {\textstyle f} omits 0 {\textstyle 0} , f has a...
Their derivation required the vector fields to decay sufficiently fast atinfinity. Later, this condition could be relaxed, and the Helmholtz decomposition...