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Arsenal came into the match having not beaten City in the league since 2015, a run of 15 games -- their longest winless streak against a single opponent in league history.
Manchester United's campaign of woe continued with a 1-0 home loss to Crystal Palace but there were no such troubles for Arsenal who, along with Spurs, closed the gap to leaders City to one point with a rampant 4-0 win at Bournemouth.
Liverpool won 3-1 while Arsenal were held 2-2 by Spurs.
Sussex received their third and fourth penalties of the season during the win over Leicestershire at Hove.
Manchester United tasted a 1-3 defeat at Old Trafford while City won by the same margin against the Hammers.
Chelsea lost at home to Nottingham Forest in the Premier League.
Both sides had a number of decent chances in the first half-hour with the best of them falling to Arsenal's Eddie Nketiah, who hit the post in the 29th minute
The 28-year-old Arrizabalaga will arrive as a temporary replacement for Thibaut Courtois, who will be sidelined for several months after suffering a torn anterior cruciate ligament in his left knee during a training session last Thursday.
Arsenal won 2-1 against Forest while Newcastle hammered Aston Villa 5-1.
Gvardiol is Pep Guardiola's second signing in this transfer window after Croatia midfielder Mateo Kovacic joined from Chelsea.