In light of the well-known theorem of Gelfand that, bluntly put, ends up saying that unital abelian C*-algebras are the 'same' as compact Hausdorff topological spaces, I tried to c …

Given two locally compact topological spaces $X$ and $Y$, and a local homeomorphism $f : X \to Y$, Gelfand duality gives us a homomorhism $Cf : C_0(Y) \to C_0(X)$. How does the fac …

The Gelfand-Neumark theorem for commutative von Neumann algebras states that the following three categories are equivalent: (1) The opposite category of the category of commutative …

The contravariant functor $C(-)$ given by $$ \hom_{Top}(-,\mathbb{R}):cCW\to Rng $$ where $cCW$ is the category of compact CW complexes is injective on objects. What is known about …