What was found
AFTER GEAR UP SELECTION, EICAS RED NOSE DOOR OPEN LIGHT ILLUMINATED. NOTICED AIR NOISE AND FOLLOWED NON-NORMAL PROCEDURES. SELECTED GEAR DOWN AND NOSE DOOR OPEN MESSAGE WENT OUT AND THEN REAPPEARED. CONTACTED ATC TO RETURN TO DEPARTURE. THE CREW THEN CONTACTED DISPATCH AND MX CONTROL TO INFORM THEM OF THE EICAS WARNING. THE RETURN TO DEPARTURE, OCCURRED UNEVENTFULLY. FOUND CLOSED SOLENOID OF NOSE GEAR DOOR SELECTOR VALVE BAD. R & R NLG DOOR SELECTOR VALVE IAW MM 32-22-00. ALL CKS GOOD IAW MM 32-22. PN ON/OFF 750006000, S/N ON 0780T, S/N OFF 0796T.