PPO- та PCO-еквівалентності неперервних відображень заданих на S¹ v S¹

Abstract

Let S¹ = {(x,y) belongs R² : x² + y² = 1} be a circle, S¹ v S¹ = (S¹ II.S¹)/~, x0 ~ y0 a topological space with a fix point and f : S¹ v S¹ → R a continuous function with a finite number oflocal extrema. We will consider two different types of equivalency of such functions and for both of them necessary and sufficient conditions for functions to be equivalent will be obtained.