Finite dimensions defined by means of $m$-coverings

Abstract

We introduce and investigate finite dimensions$(m,n)\text{-}\tx{\rm dim}$ defined by means of $m$-coverings. Thesedimensions generalize the Lebesgue dimension: $\tx{\rmdim}=(2,1)\text{-}\tx{\rm dim}$. If $n<m$ and $(m,n)\text{-}\tx{\rmdim}X<ınfty$, then $X$ is weakly infinite-dimensional in thesense of Smirnov.