2016/05/12 by Hida, Clayton Suguio
#46B26 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1605.03708
We consider the cardinal invariant bd defined by M. Džamonja and I. Juhász concerning bidiscrete systems. Using the relation between bidiscrete systems and irredundance for a compact Hausdorff space K, we prove that w(K)≤ bd(K)⋅ hL(K)+, generalizing a result of S. Todorcevic concerning the irredundance in Boolean algebras and we prove that for every maximal irredundant family F⊂ C(K), there is a π-base B for K with |F|=|B|, a result analogous to the McKenzie Theorem for Boolean algebras in the context of compact spaces. In particular, it is a consequence of the latter result that π(K)≤ bd(K) for every compact Hausdorff space K. From the relation between bidiscrete systems and biorthogonal systems, we obtain some results about biorthogonal systems in Banach spaces of the form C(K).