of an analytic function
A set of singular points (cf. Singular point) of an analytic function in the complex variables , , defined by some supplementary conditions. In particular, isolated singular points (cf. Isolated singular point) are sometimes called isolated singularities.
A set such that in a domain adjoining there is defined a single-valued analytic function for which the question arises of the possibility of analytic continuation of to . For example, let be a domain of the space , let be a compactum contained in , and let be holomorphic on . is then a possible singularity of , and the question of analytic continuation (perhaps under certain supplementary conditions) of onto the entire domain arises; in other words, the question of "elimination" or "removal" of the singularity .
See also Removable set.
Singularity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Singularity&oldid=18225