TY - JOUR
T1 - Cauchy action on filter spaces
AU - Rath, N.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - A Cauchy group (G,D, ·) has a Cauchy-action on a filter space (X,C), if it acts in a compatible manner. A new filter-based method is proposed in this paper for the notion of group-action, from which the properties of this action such as transitiveness and its compatibility with various modifications of the G-space (X,C) are determined. There is a close link between the Cauchy action and the induced continuous action on the underlying G-space, which is explored here. In addition, a possible extension of a Cauchy-action to the completion of the underlying G- space is discussed. These new results confirm and generalize some of the properties of group action in a topological context.
AB - A Cauchy group (G,D, ·) has a Cauchy-action on a filter space (X,C), if it acts in a compatible manner. A new filter-based method is proposed in this paper for the notion of group-action, from which the properties of this action such as transitiveness and its compatibility with various modifications of the G-space (X,C) are determined. There is a close link between the Cauchy action and the induced continuous action on the underlying G-space, which is explored here. In addition, a possible extension of a Cauchy-action to the completion of the underlying G- space is discussed. These new results confirm and generalize some of the properties of group action in a topological context.
KW - Cauchy map
KW - Completions
KW - Continuous action
KW - Filter space and its modifications
KW - G-space
UR - http://www.scopus.com/inward/record.url?scp=85067605500&partnerID=8YFLogxK
U2 - 10.4995/agt.2019.10490
DO - 10.4995/agt.2019.10490
M3 - Article
AN - SCOPUS:85067605500
SN - 1576-9402
VL - 20
SP - 177
EP - 191
JO - Applied General Topology
JF - Applied General Topology
IS - 1
ER -