Dowker space: Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch (New article, my own wording from Wikipedia) |
imported>Richard Pinch (remove WPmarkup; subpages) |
||
| Line 1: | Line 1: | ||
{{subpages}} | |||
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]]. | ||
| Line 5: | Line 6: | ||
==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 13:51, 29 October 2008
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