Monad Metrizable Space

Orhan Göçür
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Orhan Göçür: Department of Statistics and Computer Sciences, Faculty of Science and Literature, Bilecik Seyh Edebali University, 11000 Bilecik, Turkey

Mathematics, 2020, vol. 8, issue 11, 1-14

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.

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; P i , i = 0, 1, 2, 3, 4; parametric separation axioms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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