A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperkähler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a Gibbons-Hawking space. The possible quotients are described in terms of the monopole set in R 3 , and it is proved that every such quotient is actually Kähler. The fact that the Gibbons-Hawking spaces are the only gravitational instantons to admit isometric quotients is proved by examining the possible fundamental groups at infinity: most can be ruled out by the classification of 3-dimensional spherical space form groups, and the rest are excluded by a computation of the Rohklin invariant (in one case) or the eta invariant (in the remaining family of cases) of the corresponding space forms.

A counterexample to a theorem of J.J. Charatonik and K. Omiljanowski giving sufficient conditions for a dendrite to be contained in all of its monotone preimages is given, and a corrected version of the theorem is presented. An alternative proof is provided for a characterization of dendrites monotonely equivalent to a universal dendrite that was originally proved using the erroneous result. Finally, in response to a question by J.J. Charatonik, it is shown that a dendrite contained in all of its monotone preimages must have a discrete set of ramification points.

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