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Re: Definition of a Hausdorff space
Posted:
Mar 20, 2006 2:21 PM


"Marc Olschok" <invalid@nowhere.com> wrote in message news:48815gFitptuU1@news.dfncis.de... > William Elliot <marsh@hevanet.remove.com> wrote: > > On Sun, 19 Mar 2006, quasi wrote: > > > >On 19 Mar 2006 17:19:23 0800, "Snis Pilbor" <snispilbor@yahoo.com> > > > >> > > > >> For some reason I was almost sure the definition of a T2 space > > > >>was: "distinct points are are contained disjoint CLOSED sets". But > > > > A space is strongly Hausdorff (T_2.5) when distinct points > > are in disjoint closed neighborhoods. > > Are you trying to show 2.5 = 1 ? > > [ Consider for any pair x =/= y the respective closed neighbourhoods > C_x,y of x and F_x,y of y with C_x,y and F_x,y disjoint. > Then compute the intersection of all C_x,y ( x =/= y ) ] > > Marc
The intersection of all closed neighborhoods of a point is closed, but it may not be a neighborhood. A closed neighborhood of a point x must contain an open set that contains x.
________________________________ Eric J. Wingler (wingler@math.ysu.edu) Dept. of Mathematics and Statistics Youngstown State University One University Plaza Youngstown, OH 445550001 3309411817



