Set-theoretic topology

The space of integers has cardinality

\aleph _{0}

, while the real numbers has cardinality

2^{\aleph _{0}}

. The topologies of both spaces have cardinality

2^{\aleph _{0}}

. These are examples of cardinal functions, a topic in set-theoretic topology.

In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of Zermelo–Fraenkel set theory (ZFC).