PIPER PA28 FLT INSTRUCTOR AND STUDENTS DEPART SDL WITH THE FUEL CAPS NOT SECURED. RETURN FOR LNDG AFTER BOTH CAPS LOST INFLT.

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ENGAGED IN FLT INSTRUCTOR TRAINING; MY 2 INSTRUCTOR 'STUDENTS' HAD COMPLETED THE PREFLT INSPECTION BY THE TIME I JOINED THEM AND ADVISED ME THAT THE FBO HAD BEEN CONTACTED BY 'R/T' WITH A FUEL REQUEST. ALTHOUGH WE HAD SUFFICIENT FUEL FOR AT LEAST THE FIRST PLANNED MISSION; WE DEEMED THAT WE WERE ABLE TO FUEL FOR BOTH PLANNED ACTIVITIES THAT DAY WITHOUT THE REQUIREMENT TO REFUEL AT BASE OR DOWN RTE LATER; THUS SAVING TIME. WE WAITED BY THE ACFT FOR SOME TIME AND EVENTUALLY; MINDFUL OF OUR BLOCK TIME REMAINING; I VISUALLY INSPECTED BOTH FUEL TANKS. I ELECTED TO DELAY DEP AND CONTINUE TO WAIT FOR THE FUELER TO ARRIVE. SUBCONSCIOUSLY; IN AN EFFORT TO SAVE TIME; I BELIEVE I LEFT THE FUEL CAPS PARTIALLY OPEN; IN THE EXPECTATION THAT THE FUEL TRUCK WOULD SHORTLY ARRIVE. I WAS THEN DISTR BY A COMPANY MECH WHO HAD A BRIEF DISCUSSION WITH ME REGARDING AN UNRELATED ISSUE. FOLLOWING THIS; STILL WITHOUT ADDITIONAL FUEL; I DECIDED TO START THE FLT AND RETURN EITHER TO BASE LATER FOR FUEL OR ELSE LAND ELSEWHERE AS WE HAD ALREADY WAITED NEARLY 30 MINS. THE CREW BOARDED AND WE TAXIED; COMPLETED PRE TKOF CHKS THEN DEPARTED; CLBING ON RWY HDG. SHORTLY AFTER TKOF; THE REAR INSTRUCTOR 'STUDENT' DECLARED THAT THE PORT FUEL CAP WAS NOT SECURE WHICH IMMEDIATELY PROMPTED US TO CHK THE STARBOARD CAP. THIS WAS ALSO NOT SECURED. WE CONTINUED CLBING AND INITIATED A TURN TO A CLOSE-IN DOWNWIND; REDUCED SPD AND ADVISED ATC OF A RETURN TO THE ARPT. THE PORT FUEL CAP SHORTLY FOLLOWED BY THE STARBOARD THEN DEPARTED THE ACFT. AN UNEVENTFUL LNDG WAS MADE AT THE ARPT. MY IMMEDIATE CONCERNS ON LNDG WERE WHAT MAY HAVE BEEN BENEATH US WHEN THE CAPS FELL AS THEY WOULD HAVE DEVELOPED SIGNIFICANT ENERGY BY THE TIME THEY REACHED THE SURFACE. THE ARPT IS LOCATED IN A DENSELY POPULATED AREA.