Dowker space

Summary

A Dowker space is a normal Hausdorff space that is not countably paracompact. Equivalently, it is a normal Hausdorff space $X$ whose product $X \times [0, 1]$ with the unit interval is not normal. Such spaces show that normality is not preserved by products, even with a compact metric factor. Mary Ellen Rudin constructed a Dowker space in ZFC.