COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF

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Abstract
The basic result of this investigation may be formulated as follows. Consider the set of natural numbers in which the following relationship is introduced: n1 precedes n2 (n1 ≼ n2) if for any continuous mapping of the real line into itself the existence of a cycle of order n2 follows from the existence of a cycle of order n1. The following theorem holds.