We know that $l_{\infty}$ be banach algebra ( under pointwise multiplication and with sup norm). How to show that its maximal ideals space is totally disconnected?
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???? Ideal $\implies$ vector subspace $\implies$ arc connected. I'm losing something? – Martín-Blas Pérez Pinilla Mar 24 '17 at 13:49
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@Martín-BlasPérezPinilla. The maximal ideals are points in a space S. The Q is about the topology of S. – DanielWainfleet Mar 26 '17 at 18:04