Fürstenberg's proof of the infinitude of primes defines one of these using arithmetic sequences as a basis. Alternative definitions for these can be given by the Kuratowski closure axioms or in terms of interior algebras. Urysohn's lemma is used to construct continuous functions on normal ones. Neighborhood, convergence, and openness are generally defined using these objects, which consist a set and a (*) namesake subset of the power set of that set that includes both the empty set and the complete space and that is closed under arbitrary unions and finite intersections. Metric spaces are examples of these that satisfy the T2 separation condition also named for Hausdorff. For 10 points, name
Fürstenberg's proof of the infinitude of primes defines one of these using arithmetic sequences as a basis. Alternative definitions for these can be given by the Kuratowski closure axioms or in terms of interior algebras. Urysohn's lemma is used to construct continuous functions on normal ones. Neighborhood, convergence, and openness are generally defined using these objects, which consist a set and a (*) namesake subset of the power set of that set that includes both the empty set and the complete space and that is closed under arbitrary unions and finite intersections. Metric spaces are examples of these that satisfy the T2 separation condition also named for Hausdorff. For 10 points, name these mathematical objects, named for the branch of mathematics to which they are central, the study of properties preserved in deformations.
Fürstenberg's proof of the infinitude of primes defines one of these using arithmetic sequences as a basis.
{topologie}s [or {topological space}s]