# Questions tagged [gelfand-duality]

3 questions

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### How to understand what a 'noncommutative space' is

Whilst acquainting myself with the fundamentals of $C^*$-algebras and their $K$-theory, I read about how Gelfand Duality allows various $C^*$-algebraic concepts to be directly translated into a geometrical/topological context and vice versa. I…

user829347

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### Can one deduce Gelfand Duality from Isbell Duality?

I was reading about Isbell Duality in nLab.
It gives an example of how we have an adjunction from $TAlg$ to presheaves.
But it is not clear to me how one can deduce the Gelfand Duality from this.

W. Zhan

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### Gelfand duality restricted to the category of Stone spaces

It is well known that the category of unital commutative $C^\ast$-algebras is dually equivalent to the category $\mathbf{KHaus}$ of compact Hausdorff spaces.
I have found that restricting the Gelfand duality to the full subcategory of Stonean…

FML

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