Statement:
Let \(E\) be a set and \(f: E\to E\), then \(f\) has a fixed point if and only if \(E\) is not the union of three mutually disjoint sets \(E_1\), \(E_2\) and \(E_3\) such that \(E_i \cap f(E_i) = \emptyset\) for \(i=1, 2, 3\).
Howard_Rubin_Number: 285
Parameter(s): This form does not depend on parameters
This form's transferability is: Unknown
This form's negation transferability is: Negation Transferable
Article Citations:
Makowski-Wi'sniewski-1969: Generalization of Abian’s fixed point theorem
Abian-1968: A fixed point theorem
Baker-1964: Solution to problem 5077
Kenyon-1963: Problem 5077
Book references
Note connections: