From: wthyde1953@gmail.com   
      
   Stefan Ram wrote:   
   > William Hyde  wrote or quoted:   
   >> "A continuous function is one whose inverse maps open sets to open sets"   
   >   
   >    It might be better to ask that the preimages of open sets come   
   >    out open, because if you think about the sine function, you   
   >    can still use that test on it even though it does not have an   
   >    inverse, since that wouldn't be single-valued.   
   >   
   >    (I'm not too sure about this, but that's just what came to mind.)   
   >   
   >   
   We're getting well beyond the limits of my memory here. All I recall of   
   general topology is that I tried to use Hausdorf axioms to prove just   
   about anything.   
      
   As for measure theory, I have nightmares of hour long classes which in   
   the end succeeded only in proving that   
      
   "The unit sphere is closed in the weak* topology".   
      
   and I can no longer recall why that was of any importance.   
      
   William Hyde   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)