Dowker space

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A Dowker space is a topological space which is normal but not countably paracompact.

C.H. Dowker had characterised these spaces[1] in 1951 as those normal spaces for which the product with the unit interval is not normal, and asked whether any such space existed. M.E. Rudin constructed an example[2] in 1971, and Zoltán Balogh gave the first ZFC construction[3] of a small (cardinality continuum) example.


  1. C.H. Dowker, On countably paracompact spaces, Can. J. Math. 3 (1951) 219-224. Zbl. 0042.41007
  2. M.E. Rudin, A normal space X for which X × I is not normal, Fundam. Math. 73 (1971) 179-186. Zbl. 0224.54019
  3. Z. Balogh, A small Dowker space in ZFC, Proc. Amer. Math. Soc. 124 (1996) 2555-2560. Zbl. 0876.54016