We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular, irreducible components), and a Stein factorization theorem. Most notably, we show that a finite morphism in our category of adic spaces is automatically open if the target is normal and both source and target are of the same pure dimension. Moreover, our version of the Stein factorization theorem includes a statement about the geometric connectedness of fibers which we have not found in the literature of rigid-analytic or Berkovich spaces.

我们将刚性解析空间的几个基本几何性质转移到 adic 空间的世界，更准确地说，转移到非阿基米德域上局部（弱）有限类型的 adic 空间类别。这包括正态性、不可约性（特别是不可约成分）和斯坦因分解定理。最值得注意的是，我们表明如果目标是正常的并且源和目标都具有相同的纯维度，则进空间类别中的有限态射会自动打开。此外，我们的斯坦因分解定理版本包括关于纤维几何连通性的陈述，这是我们在刚性解析空间或伯科维奇空间的文献中没有发现的。