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Generalized monotonically T2 spaces

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Abstract

The notion of \(\mu\)-monotonically T2 spaces is introduced, which is a generation of monotone T2 separation in general topological spaces. The characterization and some properties of \(\mu\)-monotonically T2 spaces are given. Besides, the definition of the box product of the topologies is extended to generalized topologies, and we prove that the box product of \(\mu\)-monotonically T2 spaces is \(\mu\)-monotonically T2.

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Acknowledgements

The author is grateful to the anonymous referee for valuable comments and suggestions.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan, Shandong, 250061, China

    W. H. Sun

  2. School of Mathematics and Statistics, Shandong University, Weihai, Shandong, 264209, China

    W. H. Sun

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  1. W. H. Sun
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Correspondence to W. H. Sun.

Additional information

This research is supported by Natural Science Foundation of Shandong Province(Grant No. ZR2019MA051) and National Natural Science Foundation of China–Shandong joint fund (No. U1806203) and the Fundamental Research Funds for the Central Universities (No. 2019ZRJC005) and National Natural Science Foundation of China (Grant No. 11501328).

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Sun, W.H. Generalized monotonically T2 spaces. Acta Math. Hungar. 162, 32–39 (2020). https://doi.org/10.1007/s10474-020-01091-w

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  • DOI: https://doi.org/10.1007/s10474-020-01091-w

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