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The Gunners almost found themselves behind with just six seconds on the clock as Demba Ba went for a spectacular lob straight from kickoff, but Wojciech Szczesny just recovered in time to tip the effort onto the bar.
Szczesny was called into action again in the ninth minute, and again Ba was the perpetrator as he drew a good stop from the keeper with a first-time volley.
Arsenal's first chance of the match came shortly afterwards as the game got off to a frantic start, but Santi Cazorla wasted the opening by dragging his shot wide.
Jack Wilshere threatened towards the end of the opening period when he curled an effort towards goal from just outside the box, but it was easy for the keeper to save.
Ba was the star of the first 45 minutes, however, and he came close again just before the interval when he drilled an effort just wide.
The hosts had another chance to break the deadlock just two minutes after the restart when Olcay Sahan cut inside, only to curl his effort just wide when he should have scored.
Arsenal's task got a lot harder with 10 minutes remaining as Aaron Ramsey was given his marching orders courtesy of a second yellow card.
Despite their numerical disadvantage it was Arsenal who came closest to grabbing a late winner as Alex Oxlade-Chamberlain fired an effort towards goal that was tipped onto the post.