Weak geodesic topology and fixed finite subgraph theorems in infinite partial cubes II. Fixed subgraph properties and infinite treelike partial cubes

We prove that if a partial cube G contains no divergent rays, then: (i) there exists a non-empty finite convex subgraph of G which is fixed by every automorphism of G; (ii) every self-contraction of G fixes a non-empty finite isometric subgraph of G; (iii) for every commuting family F of self-contra...

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