Re: Toplologies of the Hilbert cube
- From: William Elliot <marsh@xxxxxxxx>
- Date: Wed, 30 Mar 2005 20:31:29 -0800
On Wed, 30 Mar 2005, David C. Ullrich wrote:
William Elliot <marsh@xxxxxxxxxxx> wrote:On Tue, 29 Mar 2005, David C. Ullrich wrote:William Elliot <marsh@xxxxxxxxxxx> wrote:On Tue, 29 Mar 2005, Stephen J. Herschkorn wrote:
The product, uniform, and ell-2 toplogy on the Hilbert cube are equal. The box topology on the Hilbert cube is finer that this.
Is my conclusion correct? Details: The uniform topology on R^N is that generated by the metric d(x, y) = sup(n, min(|x_n - y_n|, 1)).
This is not the produce topology for it gives you open set (-1/2,1/2)^N = B(0^N,1/2)
Nobody said that this _was_ the produce topology, nor the product topology. The assertion is that it induces the same topology on the Hilbert cube.
Why not read posts before replying to them? There's a definition of the Hilbert cube in the OP.
Oh oh, <blush>. I've been breathing too much smoke.
No no, not the nice kind. My house has been overrun with neighbors' wood smoke that's gotten so intense, that instead of thinking this thru, I'm getting a motel room for the evening. It's hard enuf to keep up with
email and simple math, much less under the conditions of the last few
days, to remain coherent and capable.
.
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