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- W2950084913 abstract "Let $f : X lo Y$ be a map of compact metric spaces. A classical theorem of Hurewicz asserts that $dim X leq dim Y +dim f$ where $dim f =sup {dim f^{-1}(y): y in Y }$. The first author conjectured that {em $dim Y + dim f$ in Hurewicz's theorem can be replaced by $sup {dim (Y times f^{-1}(y)): y in Y }$}. We disprove this conjecture. As a by-product of the machinery presented in the paper we answer in negative the following problem posed by the first author: {em Can for compact $X$ the Menger-Urysohn formula $dim X leq dim A + dim B +1$ be improved to $dim X leq dim (A times B) +1$ ?} On a positive side we show that both conjectures holds true for compacta $X$ satisfying the equality $dim(Xtimes X)=2dim X$." @default.
- W2950084913 created "2019-06-27" @default.
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- W2950084913 date "2011-12-08" @default.
- W2950084913 modified "2023-09-27" @default.
- W2950084913 title "Dimension of the product and classical formulae of dimension theory" @default.
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