One connection between this area of mathematics and number theory is Fürstenberg's proof of the infinitude of primes.
The Seifert–van Kampen theorem in the algebraic subset of this branch of mathematics describes a property of the unions of groups. One connection between this area of mathematics and number theory is Fürstenberg's proof of the infinitude of primes. Closure under arbitrary union and finite intersection is a requirement of spaces in this branch.  Properties of spaces in this field of study include metrizability, compactness, and connectedness, and pairs of objects cannot represent homeomorphisms if they have different numbers of holes. Name this branch in which a torus and a coffee cup are considered equivalent because it is not concerned with properties changed by deformations of objects.
The Seifert–van Kampen theorem in the algebraic subset of this branch of mathematics describes a property of the unions of groups.
topology