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Статья
2014

Set of ambiguous points for functions in ℝn


E. G. GanenkovaE. G. Ganenkova
Русская математика
https://doi.org/10.3103/S1066369X14060012
Abstract / Full Text

It is known that an arbitrary function in the open unit disk can have at most countable set of ambiguous points. Point ζ on the unit circle is an ambiguous point of a function if there exist two Jordan arcs, lying in the unit ball, except the endpoint ζ, such that cluster sets of function along these arcs are disjoint. We investigate whether it is possible to modify the notion of ambiguous point to keep the analogous result true for functions defined in the n-dimensional Euclidean unit ball.

Author information
  • Petrozavodsk State University, pr. Lenina 33, Petrozavodsk, 185910, RussiaE. G. Ganenkova
References
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