In [5, Lemma 5.1] we made the following claim. We claimed that if *G* is a locally compact group and

As previously reported in [4], Yuhei Suzuki pointed out that this claim is not correct and provided the counterexample

It is a priori not clear whether the invalidity of [5, Lemma 5.1] affects any of the main results of [5]. In this erratum, we show that the main example of a non-discrete

In [5, Theorem G] we claimed that given

# Proof for Theorem G.

Since
*m* and *n* and write

Denote by
*G*, and recall that *G* is an HNN-extension of *K* by
*t*-exponent sum, as used for example in [3]. Denote by

the *t*-height of
*t*-exponent sum of a terminal piece of *w*. We put

Then

Denote by
*G*, and write ρ for its root. Write
*O*. So by the arguments of [2], the group
*G* is

As explained above, [5, Theorem B] is not correct as stated. A counterexample is provided by the Burger–Mozes group
*G* on a space *X* is called *micro-supported* if for all non-empty open subsets
*X* and fixing

# Proposition 1.

*Let G be a locally compact group acting on a compact space X. Assume that the action of G has some open amenable point stabiliser and is micro-supported. Then G is not
*

# Proof.

We may assume that *X* is non-trivial, since amenable groups are not
*X* such that *g* fixes
*h* fixes

### References

[1]
R. J. Archbold and J. S. Spielberg,
Topologically free actions and ideals in discrete

[2]
P. de la Harpe and J.-P. Préaux,

[3] M. Elder and G. Willis, Totally disconnected groups from Baumslag–Solitar groups, Infinite group theory. From the past to the future, World Scientific, Singapur (2018), 51–79. Search in Google Scholar

[4]
S. Raum,

[5]
S. Raum,

[6]
Y. Suzuki,
Elementary constructions of non-discrete

**Received:**2020-12-22

**Published Online:**2021-02-20

**Published in Print:**2021-03-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.