An Introduction to Data Base Systems - download pdf or read online

oo 1 2 Cf. Proof of Theorem 6, § 4.

If Zo t E, if a connected component of Q = CD (j, Zo) - Cr- E (j, zo) contains three exceptional values w, w', w* of w = f(z) at Zo and if U is a simply connected domain containing these three values such that UC Q, then it is possible to find a perfect subset P of E, containing zo, with the following properties: (i) if CE P, then U C CD(j, C) - Cr-E(j, C); (ii) if Ct r - P and IC - zol is sufficiently small, then U n CD (j, C)=O'3• (HERVE [3J). Theorem 4. Under the same hypothesis as in Theorem 3, there exist a positive number e and, in the perfect set P defined in Theorem 3, a subset PI of the first category on P, which possess the following property: If ~ t P and if L1 is a simple curve described in D, terminating at ~, such that the diameter of CL1 (j, ~) is less than e, then ~ t Pl' In particular, all the points of P where w = f(z) admits asymptotic values belong to PI (HERVE [3J).

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An Introduction to Data Base Systems by C.J. Date


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