By Stanislaw Saks

ISBN-10: 0444408738

ISBN-13: 9780444408730

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**Sample text**

A (cf. § 1, p. 2). A set Z in the plane is said to be ·bounded if it does not con tain the point oo and if the set of absolute values of the points zeZ is bounded, i. e. if there exists a. real finite number m such that JzJ

Theory of sets. 20 diameter of a set we mean the upper bound of the distances between any two points of this set. If a is an arbitrary point of the plane and r an arbitrary non negative real number (finite 6r infinite), then we shall denote by K(a;r) - when a=ftoo satisfying the set - the set of all points z different from oo and inequality e(a,z)

Next, from the sequence {b� llk = i,2, , whose points belong to the set B<2>, we can extract 2 a subsequence lb�} lt=i,2, convergent in the space A< J. The ••• ••• ••• sequence 1 {(b� J, space b� l A. A. is therefore compact. We can regard the Cartesian m-th power r of the plane E as an example of a Cartesian product of spaces. ,z

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