View source for Dowker space

{{TEX|done}}{{MSC|54D20}}

A [[topological space]] which is [[normal space|normal]] but not [[countably paracompact]].

[[C.H. Dowker]] had characterised these space in 1951 as those normal spaces for which the product with the unit interval is not normal, and asked whether any such space existed.  [[Mary Ellen Rudin]] constructed an example in 1971, and [[Zoltán Balogh]] gave the first [[ZFC]] construction of a small ([[cardinality of the continuum]]) example.

==References==
* C.H. Dowker, "On countably paracompact spaces", ''Can. J. Math.'' '''3''' (1951) 219-224 {{ZBL|0042.41007}}
* M.E. Rudin, "A normal space $X$ for which $X \times I$ is not normal", ''Fundam. Math.'' '''73''' (1971) 179-186 {{ZBL|0224.54019}}
* Z. Balogh, "A small Dowker space in ZFC", ''Proc. Amer. Math. Soc.'' '''124''' (1996) 2555-2560. {{ZBL|0876.54016}}