Abstract

In this article, we consider some topological invariants on the state space S(A) of a C*-algebra and the notion of almost irredundant sets: A subset X of a C*-algebra A is called almost irredundant if and only if for every a ∈ X, the element a does not belong to the norm-closure of f Σn i=1 λi Πni j=1 ai,j : where ai,j ∈ X n fag and Σn i=1 jλij 6 1g. We prove that d(A) 6 2irra(A) holds for every C*-algebra, where irra(A) is the supremum of cardinalities of almost irredundant sets in A and we prove some other cardinal inequalities on the state space of a C*-algebra.