Science Mathematics

## New PDF release: Analytic Functions

Posted On March 30, 2017 at 12:39 am by / Comments Off on New PDF release: Analytic Functions

By Stanislaw Saks

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Extra resources for Analytic Functions

Sample text

A of a sufficiently high order system of squares QuQw .. ,QP without multiple boundary vertices, such that and Pr o o f. ,Ra be these squares. The set F1 is obviously con­ tained in the interior of their sum. 5) and a F1·(L;'Rk)=O. a obtained in this manner let us add all those squares of this net which con­ tain multiple boundary vertices of the system R1, R2, Hence, we • • • obtain system Q11 Q2, , Rs (cf.

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, where .