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Topic: Definition of a Hausdorff space
Replies: 6   Last Post: Mar 21, 2006 10:54 AM

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Dr. Eric Wingler

Posts: 139
Registered: 12/12/04
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
> 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

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