Let $\{{A_n}\}$ be the closed subsets of $X$, such that ${A_n} \subset \operatorname{Int}{A_{n + 1}}$ and $ \cup {A_n} = X$, if $A_1$ and all $\operatorname{cl}(A_n-A_{n-1})$ have the covering dimension at most $m$, does $X$ have the covering dimension at most $m$?
Covering dimension of the union
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dimension-theory-analysis
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0Your example should be `{\rm Int} A` rather than `\rm{Int} A`, since `\rm` doesn't take a parameter — it is simply a switch that changes the current font. – 2012-04-20