# Dowker space

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 54D20 [MSN][ZBL]

A topological space which is 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

**How to Cite This Entry:**

Dowker space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Dowker_space&oldid=39931