Hurewicz space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-03

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Hurewicz_space


00:01:35 1 History
00:02:18 2 Hurewicz's conjecture
00:03:17 3 Hurewicz's problem
00:03:58 4 Characterizations
00:04:09 4.1 Combinatorial characterization
00:07:07 4.2 Topological game characterization
00:09:58 5 Properties
00:11:34 6 References



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.746471615236586
Voice name: en-US-Wavenet-D


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematics, a Hurewicz space is a topological space that satisfies a certain basic selection principle that generalizes σ-compactness. A Hurewicz space is a space in which for every sequence of open covers 
  
    
      
        
          
            
              U
            
          
          
            1
          
        
        ,
        
          
            
              U
            
          
          
            2
          
        
        ,
        …
      
    
    {\displaystyle {\mathcal {U}}_{1},{\mathcal {U}}_{2},\ldots }
   of the space there are finite sets 
  
    
      
        
          
            
              F
            
          
          
            1
          
        
        ⊂
        
          
            
              U
            
          
          
            1
          
        
        ,
        
          
            
              F
            
          
          
            2
          
        
        ⊂
        
          
            
              U
            
          
          
            2
          
        
        ,
        …
      
    
    {\displaystyle {\mathcal {F}}_{1}\subset {\mathcal {U}}_{1},{\mathcal {F}}_{2}\subset {\mathcal {U}}_{2},\ldots }
   such that every point of the space belongs to all but finitely many sets 
  
    
      
        ⋃
        
          
            
              F
            
          
          
            1
          
        
        ,
        ⋃
        
          
            
              F
            
          
          
            2
          
        
        ,
        …
      
    
    {\displaystyle \bigcup {\mathcal {F}}_{1},\bigcup {\mathcal {F}}_{2},\ldots }
   .