Timeline for Is the pair $(C([0 \;1]),\mathbb{C})$ a consecutive pair?
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| Jan 11, 2017 at 14:57 | history | edited | Yemon Choi | CC BY-SA 3.0 |
added 200 characters in body
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| Jan 11, 2017 at 14:54 | comment | added | Yemon Choi | @AliTaghavi Well that is why I was assuming you were working with continuous homomorphisms. I agree that in general it is not obvious if a homomorphism defined on $C([0,1])$ is continuous (the Dales-Esterle counterexamples to Kaplansky's question) but in the present case we may be able to say more. Let me think about this; I retract my earlier comment on your original question. | |
| Jan 11, 2017 at 14:25 | comment | added | Ali Taghavi | Is it obvious that the kernel of $C([0 1]) \to W$ is closed? | |
| Jan 11, 2017 at 14:20 | comment | added | Yemon Choi | You mean $W$, right? I assumed you were only interested in continuous algebra homomorphisms, and then every closed ideal in $C(X)$ is given by the functions vanishing on some open subset $U$ | |
| Jan 11, 2017 at 14:02 | comment | added | Ali Taghavi | R is just a ring not necessarily a c* algebra | |
| Jan 11, 2017 at 13:21 | history | answered | Yemon Choi | CC BY-SA 3.0 |