2016/02/08 by Balka, Richárd
#26B99 #28A78 #46E15 #54F45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.1602.02609
In an earlier paper Buczolich, Elekes and the author described the Hausdorff dimension of the level sets of a generic real-valued continuous function (in the sense of Baire category) defined on a compact metric space K. Later on, the author extended the theory for maps from K to ℝn. The main goal of this paper is to generalize the relevant results for topological and packing dimensions. Let K be a compact metric space and let us denote by C(K,ℝn) the set of continuous maps from K to ℝn endowed with the maximum norm. Let dim* be one of the topological dimension dimT, the Hausdorff dimension dimH, or the packing dimension dimP. Define d*n(K)=inf\dim*(K∖ F): F⊂ K \textrm is σ-compact with dimT F