Connected and normal Hausdorff with at least two points implies cardinality at least that of the continuum
This article gives the statement, and possibly proof, of a topological space satisfying certain conditions (usually, a combination of separation and connectedness conditions) is uncountable.
- Urysohn's lemma, which, along with the T1 assumption, tells us that normal Hausdorff spaces are Urysohn spaces.
- Connected and Urysohn with at least two points implies cardinality at least that of the continuum
The proof follows directly by combining Facts (1) and (2).