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


[[Clifford Hugh Dowker|C.H. Dowker]] had characterised these spaces<ref>C.H. Dowker, On countably paracompact spaces, ''[[Canadian Journal of Mathematics|Can. J. Math.]]'' '''3''' (1951) 219-224.  [[Zentralblatt MATH|Zbl.]] 0042.41007</ref> 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|M.E. Rudin]] constructed an example<ref>M.E. Rudin, A normal space ''X'' for which ''X &times; I'' is not normal, ''[[Fundamenta Mathematicae|Fundam. Math.]]'' '''73''' (1971) 179-186.  Zbl. 0224.54019</ref> in 1971, and [[Zoltán Tibor Balogh|Zoltán Balogh]] gave the first [[ZFC]] construction<ref>Z. Balogh, A small Dowker space in ZFC, ''[[Proceedings of the American Mathematical Society|Proc. Amer. Math. Soc.]]'' '''124''' (1996) 2555-2560. Zbl. 0876.54016</ref> of a small (cardinality [[Cardinality of the continuum|continuum]]) example.
[[Clifford Hugh Dowker|C.H. Dowker]] had characterised these spaces<ref>C.H. Dowker, On countably paracompact spaces, ''[[Canadian Journal of Mathematics|Can. J. Math.]]'' '''3''' (1951) 219-224.  [[Zentralblatt MATH|Zbl.]] 0042.41007</ref> 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|M.E. Rudin]] constructed an example<ref>M.E. Rudin, A normal space ''X'' for which ''X &times; I'' is not normal, ''[[Fundamenta Mathematicae|Fundam. Math.]]'' '''73''' (1971) 179-186.  Zbl. 0224.54019</ref> in 1971, and [[Zoltán Tibor Balogh|Zoltán Balogh]] gave the first [[ZFC]] construction<ref>Z. Balogh, A small Dowker space in ZFC, ''[[Proceedings of the American Mathematical Society|Proc. Amer. Math. Soc.]]'' '''124''' (1996) 2555-2560. Zbl. 0876.54016</ref> of a small (cardinality [[Cardinality of the continuum|continuum]]) example.


==References==
==References==
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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

  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
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