Path Connectedness over Soft Rough Topological Space

Fu, Li; Fu, Hua; Liu, Zhen; You, Fei

doi:10.9734/jamcs/2019/v31i530122

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2020

2021

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“…Some researchers tried to overcome this situation by defining another soft point [11,18,21,25]. You can see the latest study examples based on Shabir and Naz's work [26][27][28][29][30][31][32]. The other way is to redefine soft set and its operations.…”

Section: Introductionmentioning

confidence: 99%

Monad Metrizable Space

Göçür

2020

Mathematics

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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.

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