In　this　paper,　the　concepts　of　omega　theta-closed　sets　and　omega　theta-open　sets　in　L　omega-spaces　are　introduced,　and　the　omega　theta-convergence　theory　of　filters　in　an　L　omega-space　is　established.　By　means　of　the　omega　theta-convergence　theory,　some　important　characterizations　with　respective　to　the　omega　theta-closed　sets,　omega　T-2　separation　and　(omega(1),　omega(2))theta-continuous　mappings　are　obtained.