point at infinity


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point at infinity

[′pȯint at in′fin·əd·ē]
(mathematics)
A single point that is adjoined to the complex plane so that it corresponds to the pole of a stereographic projection of the Riemann sphere onto the complex plane, giving the complex plane a compact topology.
References in periodicals archive ?
Let [OMEGA] [subset] H be a domain whose extended boundary contains the point at infinity and suppose that there exists a real point t [member of] R [intersection] [OMEGA] such that [OMEGA] \ (-[-[infinity], t] (or [OMEGA] \ [t, + [infinity])) is a slice domain.
The principal focus will be on what happens to the eigenstructure of the Neumann problem ([sigma] = 0) as [sigma] proceeds along rays emanating from the origin toward the point at infinity in the complex plane.
3] are coefficients in a Taylor series expansion of the inverse natural log of the total reflection coefficient -- original network plus matching network -- about a complex frequency ([rho] = [sigma] + j[omega]) point at infinity.
3] = 0} and the point at infinity 1 compose the boundary at infinity [partial derivative][H.
0]) be the image on (4) of the point at infinity on (3), then we have [X.