Ummmm, you need to get a flea spray and spray absolutely everywhere the cat goes. The eggs of the fleas drop off, fall into the carpet or rugs or blankets, then wake up and hop up as soon as a warm body passes by. This is fine as long as the cat's about but many years ago when my then cat left home, I found flea eggs lurking in safe places like that bit of the carpet just under the edge of the sofa - every time I sat down, I was bitten round the ankles. Wash the cat's bedding, treat everywhere the cat goes, just in case.