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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: G_delta
Replies: 28   Last Post: Jan 26, 2013 3:50 AM

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Butch Malahide

Posts: 885
Registered: 6/29/05
Re: G_delta
Posted: Jan 14, 2013 12:35 AM
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On Jan 13, 11:09 pm, William Elliot <ma...@panix.com> wrote:
> If p is a point in a compact Hausdorff space, is {p} a G_delta set?

Not necessarily.

Example: [0, omega_1] with the order topology. {omega_1} is not a
G_delta set.

Example: The Tychonoff product of uncountably many 2-point discrete
spaces. No singleton is a G_delta set.

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