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Re: Definition of a Hausdorff space
Posted:
Mar 20, 2006 2:21 PM
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"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 44555-0001
330-941-1817
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