Dowker space


In the mathematical field of general topology, a Dowker space is a topological space that is T4 but not countably paracompact. They are named after Clifford Hugh Dowker.
The non-trivial task of providing an example of a Dowker space helped mathematicians better understand the nature and variety of topological spaces.

Equivalences

Dowker showed, in 1951, the following:
If X is a normal T1 space, then the following are equivalent:
Dowker conjectured that there were no Dowker spaces, and the conjecture was not resolved until Mary Ellen Rudin constructed one in 1971. Rudin's counterexample is a very large space. Zoltán Balogh gave the first ZFC construction of a small example, which was more well-behaved than Rudin's. Using PCF theory, M. Kojman and S. Shelah constructed a subspace of Rudin's Dowker space of cardinality that is also Dowker.