A topological approach to the Ulam–Kakutani–Collatz conjecture

Abstract:

We give a topological approach to the Ulam–Kakutani–Collatz conjecture. In fact we prove that if (N,τf) is not a w–R0 space is equivalent to saying that the conjecture is true, τf being the topology on N given by the open sets as those subsets θ of N such that f−1(θ)⊂θ where f is the Collatz function.

Año de publicación:

2019

Keywords:

• Collatz conjecture
• Primal spaces
• Resolvable space
• Weak R spaces 0
• Supercompact space
• Alexandroff space

Fuente:

scopus

google