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Restricted cluster sets
Author(s) -
Erdös Paul,
Piranian George
Publication year - 1960
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19600220306
Subject(s) - george (robot) , citation , computer science , cluster (spacecraft) , information retrieval , library science , combinatorics , mathematics , artificial intelligence , programming language
Let f be a complex-valued function defined in the upper half-plane H. The cluuster set C(f, x) at a point x on the real axis is defined as the set of all values w (including possibly w = m) for which there exists a sequence {xJ = (x~ + i Y,J such that x, + x, yn 4 0, and f (2,) -+ WI, We use the term restricted cluster set generically: the word “restricted” indicates either that the sequence {z+J occurring in the definition above is subject to special conditions (for exampk, that it lie on a line segment), or that the cluster set C(f, x, *) is defined in terms of unions or intersections of certain “primitive” cluster sets.