The Stereographic Projection onto the Extended Complex Plane

Many times in complex analysis we need a allow for infinity to be a permissible value to handle poles and rational functions. We use the stereographic projection as a way of finding a one-to-one and onto mapping of the Riemann sphere (just the unit sphere in R^3 with the complex plane slicing though the equator). With this mapping, the one point compactification, will provide us with a topology of the extended complex plane. #mikethemathematician, #profdabkowski, #mikedabkowski, #complexanalysis, #stereographicprojection