Difference between revisions of "Dowker space"
From Encyclopedia of Mathematics
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A [[topological space]] which is [[normal space|normal]] but not [[countably paracompact]]. | A [[topological space]] which is [[normal space|normal]] but not [[countably paracompact]]. | ||
Latest revision as of 18:49, 8 December 2016
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
Dowker space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dowker_space&oldid=39931