# 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.

## 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 × 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