TY - JOUR
T1 - A note on the sensitivity of semiflows
AU - Wu, Xinxing
AU - Ma, Xin
AU - Chen, Guanrong
AU - Lu, Tianxiu
PY - 2020/2/15
Y1 - 2020/2/15
N2 - 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 (G1, X) is not sensitive for some syndetic closed submonoid G1 of G, answering negatively the Open question 3 posed in Money (2015) [13] and Question 43 posed in Miller (2017) [8].
AB - 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 (G1, X) is not sensitive for some syndetic closed submonoid G1 of G, answering negatively the Open question 3 posed in Money (2015) [13] and Question 43 posed in Miller (2017) [8].
KW - Cofinite sensitivity
KW - Product map
KW - Semiflow
KW - Sensitivity
KW - Syndetic sensitivity
KW - Topological monoid
UR - http://www.scopus.com/inward/record.url?scp=85077335860&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85077335860&origin=recordpage
U2 - 10.1016/j.topol.2019.107046
DO - 10.1016/j.topol.2019.107046
M3 - RGC 21 - Publication in refereed journal
SN - 0166-8641
VL - 271
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 107046
ER -