Round function

<p>In <a href="/facts/Topology/2EqW47cU">topology</a> and in <a href="/facts/Calculus/MEmUTYoz">calculus</a>,  a round function is a <a href="/facts/Scalar_function/8MtPTGob">scalar function</a> 
  
    
      
        M
        →
        
          
            R
          
        
      
    
    {\displaystyle M\to {\mathbb {R} }}
  
,  
over a <a href="/facts/Manifold/rXPERJtu">manifold</a> 
  
    
      
        M
      
    
    {\displaystyle M}
  
, whose <a href="/facts/Critical_point_(mathematics)/MrEk9PnY">critical points</a> form one or several <a href="/facts/Connected_space/5CUTxfoA">connected components</a>, each <a href="/facts/Homeomorphic/jMfWg3Mn">homeomorphic</a> to the <a href="/facts/Circle/9fy5ggKn">circle</a>

S
          
            1
          
        
      
    
    {\displaystyle S^{1}}
  
, also called critical loops. They are special cases of <a href="/facts/Morse-Bott_function/bJRqH8BQ">Morse-Bott functions</a>.
</p>

Round function open-in-new

Round function