Cauchy action on filter spaces


  • N. Rath University of Western Australia



continuous action, Cauchy map, G-space, filter space and its modifications, completions


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.


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Author Biography

N. Rath, University of Western Australia

School of Mathematics and Statistics


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How to Cite

N. Rath, “Cauchy action on filter spaces”, Appl. Gen. Topol., vol. 20, no. 1, pp. 177–191, Apr. 2019.



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