JavaScript - Funciones javascript ejecución

$(document).ready(function () {

    var list = [];

    function search ( keyword ) {

      $.ajax('ajax.php', {

          type: 'POST',

          dataType: 'json',

          data: {

              'keyword': keyword

            }

          }).then(function (response) {

                  return response;

              });

    };

    $('#topSearchText').keyup(function (event) {

        event.preventDefault();

        result = search($('#topSearchText').val());

        console.log(result);

        });

    });

resultado="cadena".search("a");

then(function (response) {

                  return response;

$(document).ready(function () {

    var list = [];

    function _search ( keyword ) {

      return $.ajax('ajax.php', {

          type: 'POST',

          dataType: 'json',

          data: {

              'keyword': keyword

            }

          }).then(function (response) {

                  return response;

              });

    };

    $('#topSearchText').keyup(function (event) {

        event.preventDefault();

        _search($('#topSearchText').val()).then(function(result){

            console.log(result);

        });

    });

});