## Automorphism groups of complements of points.(English)Zbl 0829.20052

For a given group $$G$$, two directed graphs (or metrizable topological spaces) $$K_1$$ and $$K_2$$ are given such that the automorphism groups of $$K_1$$ and $$K_2$$ consist of the identity map, and for any $$x\in K_1$$, the automorphism group of $$K_1\setminus\{x\}$$ is isomorphic to $$G$$, and there exists $$x_G\in K_2$$ such that the automorphism group of $$K_2\setminus\{x_G\}$$ is isomorphic to $$G$$, and for any $$x\in K_2\setminus\{x_G\}$$, the automorphism group of any $$K_2\setminus\{x\}$$ consists of the identity.
Reviewer: V.Koubek (Praha)

### MSC:

 20F29 Representations of groups as automorphism groups of algebraic systems 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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