Fine Topology (potential Theory)
In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, only smooth functions were considered, namely those for which where is the Laplacian. In that case it was natural to consider only the Euclidean topology, but with the advent of upper semi-continuous subharmonic functions introduced by F. Riesz, the fine topology became the more natural tool in many situations.
Read more about Fine Topology (potential Theory): Definition, Observations, Properties of The Fine Topology
Famous quotes containing the word fine:
“The perception of the comic is a tie of sympathy with other men, a pledge of sanity, and a protection from those perverse tendencies and gloomy insanities in which fine intellects sometimes lose themselves. A rogue alive to the ludicrous is still convertible. If that sense is lost, his fellow-men can do little for him.”
—Ralph Waldo Emerson (1803–1882)