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La dimension de la frontière d'un ensemble analytique dans son saturé par une application

Marcos Sebastiani (1981)

Annales de l'institut Fourier

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

Local cohomological properties of homogeneous ANR compacta

V. Valov (2016)

Fundamenta Mathematicae

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...

Local cohomology and the connectedness dimension in algebraic varieties.

Markus Brodmann, Josef Rung (1986)

Commentarii mathematici Helvetici

Locally constant functions

Joan Hart, Kenneth Kunen (1996)

Fundamenta Mathematicae

Let X be a compact Hausdorff space and M a metric space. $E_{0} (X, M)$ is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which $E_{0} (X, M)$ is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of $E_{0} (X, M)$ as a normed linear space. We also build three first countable Eberlein...

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