On saddle points of continuous functions on the closed 2-disk (in Ukrainian)

Author
Ye.O.Polulyakh
Institute of Mathematics, NAS of Ukraine
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.
Keywords
saddle point, continuous function, closed 2-disk
DOI
doi:10.30970/ms.31.2.172-182
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
Volume
31
Issue
2
Year
2009
Journal
Matematychni Studii
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