Bounded normal generation is not equivalent to topological bounded normal generation

We show that some derived L¹ full groups provide examples of non simple Polish groups with the topological bounded normal generation property. In particular, it follows that there are Polish groups with the topological bounded normal generation property but not the bounded normal generation property.European Research Council (ERC CoG) No. 614195 and by ERC CoG No. 681207 y Research supported by Project ANR-14-CE25-0004 GAMME and Projet ANR-17- CE40-0026 AGRUMEpeerReviewe