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184 Let $M_0 \to M_1 \to \cdots \to M_m = X$ be a gluing decomposition of $X$, |
184 Let $M_0 \to M_1 \to \cdots \to M_m = X$ be a gluing decomposition of $X$, |
185 and let $M_0^0,\ldots,M_0^k$ be the connected components of $M_0$. |
185 and let $M_0^0,\ldots,M_0^k$ be the connected components of $M_0$. |
186 We say that a field |
186 We say that a field |
187 $a\in \cF(X)$ is splittable along the decomposition if $a$ is the image |
187 $a\in \cF(X)$ is splittable along the decomposition if $a$ is the image |
188 under gluing and disjoint union of fields $a_i \in \cF(M_0^i)$, $0\le i\le k$. |
188 under gluing and disjoint union of fields $a_i \in \cF(M_0^i)$, $0\le i\le k$. |
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189 Note that if $a$ is splittable in the sense then it makes sense to talk about the restriction of $a$ of any |
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190 component $M'_j$ of any $M_j$ of the decomposition. |
189 |
191 |
190 In the example above, note that |
192 In the example above, note that |
191 \[ |
193 \[ |
192 A \sqcup B \sqcup C \sqcup D \to (A \cup B) \sqcup (C \cup D) \to A \cup B \cup C \cup D |
194 A \sqcup B \sqcup C \sqcup D \to (A \cup B) \sqcup (C \cup D) \to A \cup B \cup C \cup D |
193 \] |
195 \] |