\[
  tV = V_t, \qquad 0 \leq t \leq 1,
\]

\[
  X \smallsetminus \mathcal{S}_t \;=\; \underbrace{W_t^{0}}_{\text{int. de } W_t} \sqcup \underbrace{W'_t}_{\text{ext. de } W_t} \qquad \text{somme topologique}
\]

\[
    \mathcal{U}_{A,C}, \quad \mathcal{U}_{B,C}, \qquad A \subset \mathcal{U}_{A,C}, \quad B \subset \mathcal{U}_{B,C}
  \]

\[
  X = X_{a,c} \amalg_c \underbrace{X_{c,b}}_{\overset{\text{déf}}{=} X_{b,c}}
\]

\[
  X_{c,b} = X_{c,d} \amalg_d \underbrace{X_{d,b}}_{\overset{\text{déf}}{=} X_{b,d}}
\]

\[
  X = \underbrace{X_{a,c} \amalg_c X_{c,d}}_{X_{a,d}} \amalg_d X_{d,b}
\]

\[
  h_{21} : \mathrm{ex}(F_1) \simeq \mathrm{or}(F_2), \qquad h_{32} : \mathrm{ex}(F_2) \simeq \mathrm{or}(F_3).
\]

\[
  A \subset A' \quad \text{et} \quad B \subset B' .
\]

\[
  \struck{D, B, C} \Longrightarrow \struck{C, A, D} \Longrightarrow \struck{D, B, C}
\]

\[
  I \times B^{n-1} \simeq B^n
\]

\[
  Z \mapsto \mathrm{Comp}(Z) = \mathrm{Hom}_{\mathrm{cont}}(Z, \{0,1\}) \;\bigl(= \Gamma(Z, \mathbb{F}_{2,Z})\bigr)
\]

\[
  \underbrace{\mathrm{Rives}(A,X)}_{\text{ens. des rives de } A \text{ dans } X} = \varinjlim_{V \text{ voisinage de } A \text{ dans } X} \mathrm{Comp}(V \smallsetminus A) = \varinjlim_{V} \Gamma(V, i_*(\mathbb{F}_{2,U}))
\]

\[
  \mathrm{Riv}(A,X) \simeq \mathrm{Comp}(S_{A,X})
\]

\[
  \Gamma(A, F|A) = \varinjlim_{V \in \mathcal{V}(A,X)} F(V)
\]

\[
  \mathrm{Comp}(\widetilde{A}) \simeq \Gamma(A, i_*(\mathbb{F}_{2,U}))
\]

\[
  (*) \qquad \mathrm{Riv}(A,X) \longrightarrow \mathrm{Comp}(\widetilde{A})
\]

\[
  \rho + \rho' = 1
\]

\[
  \widetilde{X} \amalg_{\widetilde{A}_1} (\widetilde{A}_1 \to A) \amalg_{\widetilde{A}_2} (\widetilde{A}_2 \to A),
\]

\[
  \overline{X} = \mathrm{Dec}_{\beta}(A, X),
\]

\[
  \overline{X} \longrightarrow X
\]

\[
  \overline{X} \smallsetminus \underbrace{\{A_\rho \cup A_{\rho'}\}}_{A \times \beta} \longrightarrow X \smallsetminus A
\]

\[
  A_\rho \xrightarrow{\ \simeq\ } A, \qquad A_{\rho'} \xrightarrow{\ \simeq\ } A,
\]

\[
  A \times \beta \longrightarrow A
\]