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Monad Metrizable Space

Author

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  • Orhan Göçür

    (Department of Statistics and Computer Sciences, Faculty of Science and Literature, Bilecik Seyh Edebali University, 11000 Bilecik, Turkey)

Abstract

Do the topologies of each dimension have to be same and metrizable for metricization of any space? I show that this is not necessary with monad metrizable spaces. For example, a monad metrizable space may have got any indiscrete topologies, discrete topologies, different metric spaces, or any topological spaces in each different dimension. I compute the distance in real space between such topologies. First, the passing points between different topologies is defined and then a monad metric is defined. Then I provide definitions and some properties about monad metrizable spaces and PAS metric spaces. I show that any PAS metric space is also a monad metrizable space. Moreover, some properties and some examples about them are presented.

Suggested Citation

  • Orhan Göçür, 2020. "Monad Metrizable Space," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1891-:d:438036
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    References listed on IDEAS

    as
    1. Ping Zhu & Qiaoyan Wen, 2013. "Operations on Soft Sets Revisited," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, January.
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