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Fabianski, who will play for the Gunners in Tuesday night's Carling Cup showdown with Tottenham at White Hart Lane, has rarely looked comfortable in first team action and came in for much criticism for his performances last season.
But Wenger, who is always supportive of his young players, believes the Polish 'keeper has what it takes to make it to the top of the game.
"I am personally convinced he is a world-class goalkeeper, potentially, and of course when you have that potential you want to transfer that into competitive games,'' Wenger added. "I can only give him the opportunity to give him games to show what I believe about how good he is.
"I believe he has a very strong attitude, very strong response and he works very hard in training, so he has an opportunity to show his massive talent. I have massive faith in him and I think I have shown this historically. I am convinced he will become a great goalkeeper.
"We live in a world where if you have an opportunity you have to take it. You will get a second one, but you will not get 10 - and that is part of our job.''