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user9072
user9072

To be specific, my question is as follows:

Question: Let X$X$ be an inverse limit of compact metric spaces (X_i, d_i)$(X_i, d_i)$, then does it hold

dim(X, d) \leq sup_i {dim (X_i, d_i)}$\dim(X, d) \leq \sup_i \{\dim (X_i, d_i)\}$ for some compatible metric d$d$ on X$X$?

To be specific, my question is as follows:

Question: Let X be an inverse limit of compact metric spaces (X_i, d_i), then does it hold

dim(X, d) \leq sup_i {dim (X_i, d_i)} for some compatible metric d on X?

To be specific, my question is as follows:

Question: Let $X$ be an inverse limit of compact metric spaces $(X_i, d_i)$, then does it hold

$\dim(X, d) \leq \sup_i \{\dim (X_i, d_i)\}$ for some compatible metric $d$ on $X$?

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Bingbing Liang
Bingbing Liang
  • 1

Is there any result concerning on the metric dimension of inverse limit?

To be specific, my question is as follows:

Question: Let X be an inverse limit of compact metric spaces (X_i, d_i), then does it hold

dim(X, d) \leq sup_i {dim (X_i, d_i)} for some compatible metric d on X?