Abstract
The generalized topology on the Cartesian product of sets can be defined by the generalized topology on the factors of the product. A G-method on a set can derive a generalized topology, which is called a G-generalized topology. On the one hand, we introduce the concept of product G-methods on sets which lead to a G-generalized topology on the Cartesian products that is different both from the Császár and the Eckhoff product of G-generalized topologies on the factors. On the other hand, we study the G-connectedness of the Cartesian products and prove that a G-connectedness determined by an almost pointwise method is countably multiplicative. The countably multiplicative property of sequentially connected spaces is extended.
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Acknowledgements
This paper is dedicated to Professor Shou Lin’s 60th birthday. The authors are grateful to Professor Shou Lin for his meticulous guidance in writing this article. We would like to thank the referee for the detailed list of corrections, suggestions to the paper, and all her or his efforts in order to improve the paper. For example, the referee gives some more and earlier references to generalized topologies, introduces the Eckhoff product, and points out some gaps in Lemma 2.4 and Example 3.2.
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This research is supported by NSFC (No. 11801254) and Scientific Research and Innovation Team Project of Ningde Normal University (2017T01).
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Liu, L., Ping, Z. Product Methods And G-Connectedness. Acta Math. Hungar. 162, 1–13 (2020). https://doi.org/10.1007/s10474-020-01086-7
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DOI: https://doi.org/10.1007/s10474-020-01086-7