In this paper the
relationships existing among the Boolean σ-algebra generated by the open central
projections of the enveloping von Neumann algebra ℬ of a C∗-algebra 𝒜, the Borel
structure induced by a natural topology on the quasispectrum of 𝒜, and the type of
𝒜 are discussed. The natural topology is the hull-kernel topology. It is shown that
this topology is induced by the open central projections and is the quotient topology
of the factor states of 𝒜(with the relativized w∗-topology) under the relation of
quasi-equivalence. The Borel field is shown to be Borel isomorphic with the
Boolean σ-algebra multiplied by the least upper bound of all minimal central
projections. Finally, it is shown that 𝒜 is GCR if and only if the Boolean
σ-algebra (resp. algebra) contains all minimal projections in the center of ℬ,
or equivalently, if and only if every point in the quasi-spectrum is a Eorel
set.
