Re: question on compactification


hagman wrote:
Darren schrieb:

Is there a way to introduce a compactification on R such that the
elements form a group with respect to multiplication?

Apparently you cannot have that, as no matter what kind of points you
add, you would still have 1*0 = 0 = 0*0 for the points already there.

Yeah, I was thinking that might be a sticking point.
I had thought about defnining:
0*oo = 1

in order to force 0 to have a multiplicative inverse, but then I think
that screws up the distributive property.

So to make your question more precise:
Do you want a compact topological space X and a topological group G
such that G and R are subspaces of X and (G intersect R) is R* and X =
G union R?

You are getting a little beyond me :) What is R* here?

.

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