Finite dimensions defined by means of $m$-coverings
Keywords:
Dimension, dimension $(m, n)\text{-}\tx{\rm dim}$, metrizable space, hereditarily normal spaceSubjects:
54F45Abstract
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.
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2012-10-15
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