Soit $f:U\to V$ une application analytique propre entre des ouverts de ${\mathbf{C}}^n$, soit $X$ un sous-ensemble analytique de $U$ et soit $Z=f^{-1}\left(f\right(X\left)\right)$. On donne des conditions pour que $\overline{Z-X}\cap X$ soit de codimension 1 dans $X$.

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary ${}^{n-1}$. We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...