Metrizable space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-03-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Metrization_theorem


00:00:59 1 Properties
00:01:41 2 Metrization theorems
00:04:30 3 Examples
00:05:08 4 Examples of non-metrizable spaces
00:06:08 5 See also



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SUMMARY
=======
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space 
  
    
      
        (
        X
        ,
        
          
            T
          
        
        )
      
    
    {\displaystyle (X,{\mathcal {T}})}
   is said to be metrizable if there is a metric 

  
    
      
        d
        :
        X
        ×
        X
        →
        [
        0
        ,
        ∞
        )
      
    
    {\displaystyle d\colon X\times X\to [0,\infty )}
  such that the topology induced by d is 
  
    
      
        
          
            T
          
        
      
    
    {\displaystyle {\mathcal {T}}}
  . Metrization theorems are theorems that give sufficient conditions for a topological space to be metrizable.