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Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 6, Pages 3–8 (Mi ivm8899)  

On a set of ambiguous points of a functions in the $\mathbb R^n$

E. G. Ganenkova

Chair of Mathematical Analysis, Petrozavodsk State University, 33 Lenin Ave., Petrozavodsk, 185910 Russia

Abstract: It is known that an arbitrary function in the open unit disk can have at most countable set of ambiguous points. Point $\zeta$ 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 $\zeta,$ 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.

Keywords: cluster set, ambiguous point.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:6, 1–5

Document Type: Article
UDC: 517.518
Received: 30.11.2012

Citation: E. G. Ganenkova, “On a set of ambiguous points of a functions in the $\mathbb R^n$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 6, 3–8; Russian Math. (Iz. VUZ), 58:6 (2014), 1–5

Citation in format AMSBIB
\Bibitem{Gan14}
\by E.~G.~Ganenkova
\paper On a set of ambiguous points of a~functions in the~$\mathbb R^n$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 6
\pages 3--8
\mathnet{http://mi.mathnet.ru/ivm8899}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 6
\pages 1--5
\crossref{https://doi.org/10.3103/S1066369X14060012}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84900840770}


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