Small-bias sample space
My name is Jestine (34 years old) and my hobbies are Origami and Microscopy.
Here is my web site; http://Www.hostgator1centcoupon.info/ (support.file1.com) In the mathematical field of general topology, a Dowker space is a topological space that is T4 but not countably paracompact.
If X is a normal T1 space (a T4 space), then the following are equivalent:
- X is a Dowker space
- The product of X with the unit interval is not normal. C. H. Dowker 1951
- X is not countably metacompact. This was also shown by Dowker, according to Balogh.
Dowker conjectured that there were no Dowker spaces, and the conjecture was not resolved until M.E. Rudin constructed one in 1971. Rudin's counterexample is a very large space (of cardinality ) and is generally not well-behaved. Zoltán Balogh gave the first ZFC construction of a small (cardinality continuum) example, which was more well-behaved than Rudin's. Using PCF theory, M. Kojman and S. Shelah constructed a subspace of Rudin's Dowker space of cardinality that is also Dowker.
- 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
- M. Kojman, S. Shelah: "A ZFC Dowker space in : an application of PCF theory to topology", Proc. Amer. Math. Soc., 126(1998), 2459-2465.