COMBINATORY INVARIANT FOR FUNCTION DETERMINED ON A CIRCLE
Journal Title: Енергетика і автоматика - Year 2018, Vol 0, Issue 6
Abstract
The article deals with the case of continuous functions with a finite number of local extreme a defined on a one-dimensional compact manifold without boundary. The conditions of topological equivalence of continuous functions on S1 are investigated. A combinatorial invariant for the function f is constructed and it is determined that for the class of functions in question the complete combinatorial invariants must coincide. It is shown that for an arbitrary function f there exists up to a cyclic order of arcs, a single partition and it is proved that a necessary and sufficient condition for the topological equivalence of two functions on a circle is an isomorphism of their partitions.
Authors and Affiliations
Т. Г. КРИВОРОТ
Keywords
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