in which city will you find 45th street station (bmt fourth avenue line)?
New York City.
45th Street station (BMT Fourth Avenue Line)
45th Street is a local station on the BMT Fourth Avenue Line of the New York City Subway. 
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45th Street station (BMT Fourth Avenue Line) [SEP] Introduction
45th Street is a local station on the BMT Fourth Avenue Line of the New York City Subway. Located at 45th Street and Fourth Avenue in Sunset Park, Brooklyn, it is served by the R train at all times. The N train also stops here during late nights, and some rush-hour W trains stop here in the peak direction. The 45th Street station was constructed as part of the Fourth Avenue Line, which was approved in 1905. Construction on the segment of the line that includes 45th Street started on March 15, 1913, and was completed in 1915. The station opened on September 22, 1915, after the opening of the initial portion of the BMT Fourth Avenue Line to 59th Street.