On~Aleksandrov's obstruction theorem

I. A. Shvedov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 31 (1976) no. 5, pp. 192-197

Résumé

The following two results ate proved. Theorem 1. {\it Let $X$ be a subspace of a locally compact metric space with $\dim_{\mathscr G}X=p$, and $A$ the subset consisting of all points $a\in X$ such that $H^p(X,X\setminus U;\mathscr G)\ne 0$ for every sufficiently small open ball $U$ with centre at $a$. Then $\dim_{\mathscr G}A=p$}. Theorem 2. {\it Let $X$ be a metric space, $\dim_{\mathscr G}X=p$, and $Y$ the subspace of $X$ consisting of all points $y\in X$ that have a basis of open neighbourhoods $\mathscr B(y)$ точки $y$ such that for each $U\in \mathscr B(y)$ the group $H^p(X,X\setminus U;\mathscr G)$ is not trivial. Then $\dim_{\mathscr G}Y=p$}.