Keywords: فضای کم فضای کم; primary, 40A35; secondary, 40A05, 26A03, 54A20, 54F65Ideal; Filter; P-ideal; Coideal; Ideal convergence; Filter convergence; II-convergence; Sequentially compact space; Countably compact space; Hindman theorem; van der Waerden theorem; Hindman space; van