On saddle points of continuous functions on the closed 2-disk (in Ukrainian) |
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| Author |
polulyah@imath.kiev.ua
Institute of Mathematics, NAS of Ukraine
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| Abstract |
We discuss definitions of regular, critical and saddle points of continuous functions on the plane. Two different definitions of a regular point are given. The example is constructed of a continuous non-negative function on the closed 2-disk $D^2$ which vanishes at its boundary and has exactly two local extrema in $Int{D^2}$ and has no saddle points.
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| Keywords |
saddle point, continuous function, closed 2-disk
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| DOI |
doi:10.30970/ms.31.2.172-182
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Reference |
1. M. H. A. Newman, Elements of the topology of plane sets of points -- Cambridge: Cambridge Univ. Press, 1964 -- 214 pp.
2. Х. Цишанг, Э. Фогт, Х.--Д. Колдевай, Поверхности и разрывные группы: Пер. с англ. -- М.: Наука, 1988. -- 688 с. 3. В.А.~Рохлин, Д.Б.~Фукс, Начальный курс топологии. Геометрические главы-- М.: Наука, 1977. -- 488 с. |
| Pages |
172-182
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| Volume |
31
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| Issue |
2
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| Year |
2009
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| Journal |
Matematychni Studii
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