ACR LANDS ON RWY NOTAMED CLOSED BUT CONFIRMED BY ARPT MGR OFFICE TO BE OPEN AND CLR.

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MY FLT DEPARTED RSW FOR SRQ. BOTH RSW AND SRQ TWRS WERE CLOSED. RWY 14-32 AT SRQ WAS NOTAMED CLOSED ON MY FLT PLAN. TAMPA APCH ASKED ME WHAT RWY I WOULD LIKE. I TOLD HIM 14. HE VECTORED ME FOR A R DOWNWIND TO RWY 14 AT SRQ. WE MADE A CALL TO THE COMPANY RAMP CTL FREQ AT SRQ TO VERIFY THE STATUS OF RWY 14. WE HAD HEARD A DISCUSSION ON THE TAMPA APCH FREQ ABOUT POSSIBLE WORK BEING DONE ON RWY 14-32 AT SRQ. OUR RAMP PERSONNEL VERIFIED WITH THE ARPT OPS MGR'S OFFICE THAT THE RWY WAS OPEN AND CLR. THEY RPTED THIS TO US. ALL APPROPRIATE 'TWR CLOSED' RPTS WERE MADE ON THE CTAF. RWY 14 ILS WAS TUNED ON OUR RECEIVERS IT WAS OPERATIONAL AND IDENTED. THE RWY 14 LIGHTS RESPONDED TO THE KEYING OF OUR TRANSMITTER ON THE CTAF. TAMPA APCH CLRED US FOR AN APCH TO RWY 14. WE MADE A NORMAL LNDG. ON ROLL OUT WE NOTICED WORKMEN; WHO HAD BEEN PAINTING YELLOW STRIPES ON THE RWY 14 OVERRUN; WERE CLR OF THE AREA. THEY HAD BEEN MONITORING THE CTAF AND HAD BEEN NOTIFIED OF OUR ARR BY OUR COMPANY RAMP PERSONNEL THROUGH THE ARPT OPS MGR'S OFFICE.