Revistes Catalanes amb Accés Obert (RACO)

Topological automorphism groups of chains

Sergei V. Ovchinnikov


It is shown that any set--open topology on the automorphism group $A(X)$ of a chain $X$ coincides with the pointwise topology and that $A(X)$ is a topological group with respect to this topology. Topological properties of connectedness and compactness in $A(X)$ are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.

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