On stratified L-valued filters induced by ⊤-filters

A problem stated by Höhle in his book “Many-valued Topology and Applications” is solved. The problem consists of finding a necessary and sufficient condition for a stratified L-filter to be induced by a ⊤-filter in the sense of Lemma 4.4.3 in this book. The condition given is proved to be equivalent to the condition considered in Proposition 4.4.4 in this book in the case of complete MV-algebras with square roots. We also extend the relation between stratified L-filters and ⊤-filters, established earlier by Höhle and Šostak, to stratified and tight L-filters.