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edit approved Dec 7, 2018 at 14:58
Rad80
edit approved Dec 7, 2018 at 14:58
Rad80
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homotopy and (co)filtered limits.

Suppose we have a (co)filtered digaram $\dots \rightarrow X_{2}\rightarrow X_{1}$ of topological space. Is is true that the natural map $\pi_{0}[\mathrm{lim }\textrm{ X_{i}}]\rightarrow \mathrm{lim} \pi_{0}(\textrm{ X_{i}})$$\pi_{0}[\lim X_{i}]\rightarrow \lim \pi_{0}(X_{i})$ is an isomorphism ?

homotopy and (co)filtered limits.

Suppose we have a (co)filtered digaram $\dots \rightarrow X_{2}\rightarrow X_{1}$ of topological space. Is is true that the natural map $\pi_{0}[\mathrm{lim }\textrm{ X_{i}}]\rightarrow \mathrm{lim} \pi_{0}(\textrm{ X_{i}})$ is an isomorphism ?

homotopy and (co)filtered limits

Suppose we have a (co)filtered digaram $\dots \rightarrow X_{2}\rightarrow X_{1}$ of topological space. Is is true that the natural map $\pi_{0}[\lim X_{i}]\rightarrow \lim \pi_{0}(X_{i})$ is an isomorphism ?

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Ofra
Ofra
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homotopy and (co)filtered limits.

Suppose we have a (co)filtered digaram $\dots \rightarrow X_{2}\rightarrow X_{1}$ of topological space. Is is true that the natural map $\pi_{0}[\mathrm{lim }\textrm{ X_{i}}]\rightarrow \mathrm{lim} \pi_{0}(\textrm{ X_{i}})$ is an isomorphism ?