Göçür and Kopuzlu showed that any soft space, may not be a soft space (also may not be a soft space). In this case, they described a new soft separation axiom which is called soft n-space. Then they indicated that any soft n-space is soft space also (Göçür and Kopuzlu, 2015b). In the present paper we showed that if is a soft space, topological space is a space for all. Then we indicated that any Soft Metric space is also soft nspace. Consequently, we indicated that any Soft Metric space Soft n-space Soft space Soft space soft space soft space also.
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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