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On some fundamental problems in cluster set theory


Author: J. A. Eidswick
Journal: Proc. Amer. Math. Soc. 39 (1973), 163-168
MSC: Primary 26A15; Secondary 30A72
DOI: https://doi.org/10.1090/S0002-9939-1973-0313454-X
MathSciNet review: 0313454
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Abstract: An attempt to characterize the local behavior of arbitrary functions of two real variables in terms of their cluster sets along various approach curves leads to two main problems: (1) Finding a ``small'' family $ {\Gamma _0}$ of approach curves such that cluster sets along $ {\Gamma _0}$ determine total cluster sets; (2) Finding a ``large'' family of approach curves along which cluster sets can be preassigned. A nice solution of (1) is found and (2) is partially solved. Conjectures are made concerning a link between (2) and sets which are always of the first category.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313454-X
Keywords: Cluster sets, approach curves, truncations, sets which are always of the first category
Article copyright: © Copyright 1973 American Mathematical Society

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