A note on the sensitivity of semiflows

In this note, it is shown that there exist two non-syndetically sensitive cascades defined on complete metric spaces whose product is cofinitely sensitive, answering negatively the Question 9.2 posed in Miller and Money (2017) [12]. Moreover, it is shown that there exists a syndetically sensitive semiflow ( G , X ) defined on a complete metric space X such that ( G 1 , X ) is not sensitive for some syndetic closed submonoid G 1 of G, answering negatively the Open question 3 posed in Money (2015) [13] and Question 43 posed in Miller (2017) [8].