New PDF release: Analytic Functions
By Stanislaw Saks
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Extra resources for Analytic Functions
More generally, if the complement of a region has exactly n com ponents, then the region is said to be n-tuply connected (the num ber n of components may be infinite: the region is then termed infinitely connected); the number n, finite or infinite, is called the degree of connectivity of the region. , are examples of simply connected regions. Annuli, and in particular - an nular neighbourhoods, are doubly connected regions. The open plane, after removing from it the sequence of points 1,2, • .
Am, we mean the set of all § 13 41 Cartesian product of sets. a1,a ,... ,am), where a1' a2, ,am, are re 2 A1,A ,... ,Am. =A =A, m m by Am; the set A"' will be called the Cartesian m-th power (and hence e. g. in the case m 2 the Cartesian square) of the set A . x A<"'> systems of the form ( • • • spectively. elements of the sets • • = • . will be considered an abstract space by associating with it, as 2l of all sets of the form v<1>E2l(l), v<2>E2l<2>, , ycm)E2l("') . a system of neighbourhoods, the family V=V<1>x v<2>x xv