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تسجيل مستخدم جديدHomogeneous ANR-spaces and Alexandroff manifolds
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تأليف
V. Valov
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We specify a result of Yokoi cite{yo} by proving that if $G$ is an abelian group and $X$ is a homogeneous metric $ANR$ compactum with $dim_GX=n$ and $check{H}^n(X;G) eq 0$, then $X$ is an $(n,G)$-bubble. This implies that any such space $X$ has the following properties: $check{H}^{n-1}(A;G) eq 0$ for every closed separator $A$ of $X$, and $X$ is an Alexandroff manifold with respect to the class $D^{n-2}_G$ of all spaces of dimension $dim_Gleq n-2$. We also prove that if $X$ is a homogeneous metric continuum with $check{H}^n(X;G) eq 0$, then $check{H}^{n-1}(C;G) eq 0$ for any partition $C$ of $X$ such that $dim_GCleq n-1$. The last provides a partial answer to a question of Kallipoliti and Papasoglu cite{kp}.
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