Text this: Green's relations on a semigroup of transformations with restricted range that preserves an equivalence relation and a cross-section

  _____    _    _     ______    ______    _____   
 / ____|| | || | ||  /_____//  /_   _//  |__  //  
/ //---`' | || | ||  `____ `    -| ||-     / //   
\ \\___   | \\_/ ||  /___//     _| ||_    / //__  
 \_____||  \____//   `__ `     /_____//  /_____|| 
  `----`    `---`    /_//      `-----`   `-----`  
                     `-`