Abstract
Abstract Given a topological đș-space, we consider equations with constants over đș. In particular, we formulate some very general conditions on words with constants w âą ( y Ì , g Ì ) w(\bar{y},\bar{g}) over đș which guarantee that the inequality w âą ( y Ì , g Ì ) â 1 w(\bar{y},\bar{g})\neq 1 has a solution in đș. These results are illustrated in some typical situations. In particular, standard actions of Thompsonâs group đč and branch groups are considered.
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