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Open AccessArticle

Monad Metrizable Space

Department of Statistics and Computer Sciences, Faculty of Science and Literature, Bilecik Seyh Edebali University, 11000 Bilecik, Turkey
Mathematics 2020, 8(11), 1891; https://doi.org/10.3390/math8111891
Received: 18 September 2020 / Revised: 19 October 2020 / Accepted: 20 October 2020 / Published: 31 October 2020
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. View Full-Text
Keywords: soft set theory; soft metric space; amply soft set; amply soft monad point; AS topology; PAS topology; PAS metric space; monad metrizable space; monad metric space; Pi, i = 0, 1, 2, 3, 4; parametric separation axioms soft set theory; soft metric space; amply soft set; amply soft monad point; AS topology; PAS topology; PAS metric space; monad metrizable space; monad metric space; Pi, i = 0, 1, 2, 3, 4; parametric separation axioms
MDPI and ACS Style

Göçür, O. Monad Metrizable Space. Mathematics 2020, 8, 1891. https://doi.org/10.3390/math8111891

AMA Style

Göçür O. Monad Metrizable Space. Mathematics. 2020; 8(11):1891. https://doi.org/10.3390/math8111891

Chicago/Turabian Style

Göçür, Orhan. 2020. "Monad Metrizable Space" Mathematics 8, no. 11: 1891. https://doi.org/10.3390/math8111891

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