Formally, and within the general scope of functional analysis, an isolated singularity for a function f is any " topologically isolated " point within an open set where the function is defined.
12.
Then " g " has an isolated singularity at " x " 0, and maps the boundary of some deleted neighborhood of " x " 0 to the unit sphere.
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W Pardon and M Stern, Pure hodge structure on the L2-cohomology of varieties with isolated singularities, Journal fur die Reine und Angewandte Mathematik, vol . 533 ( 2001 ), pp . 55 80
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Wall's work since the mid-1970s has mostly been in singularity theory as developed by R . Thom, J . Milnor and V . Arnold, and especially concerns the classification of isolated singularities of differentiable maps and of algebraic varieties.
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Bers proved an extension of Riemann's theorem on removable singularities, showing that any isolated singularity of a pencil of minimal surfaces can be removed; he spoke on this result at the 1950 International Congress of Mathematicians and published it in " Annals of Mathematics ".
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The series you have calculated is the Laurent expansion of sin ( 1 / z ) about the origin, and there is a theorem that says that the principal part of the Laurent expansion ( the part with the negative powers ) about an isolated singularity is an infinite sum if and only if the singularity is essential.
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A " measured foliation " ( \ mathcal F, \ mu ) on S is a foliation \ mathcal F on S which may admit isolated singularities, together with a " transverse measure " \ mu, i . e . a function which to each each arc \ alpha transverse to the foliation \ mathcal F associates a positive real number \ mu ( \ alpha ).
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