Can catfleas breed if there is no cat in the house ?

i have recently been having a problem with cat fleas. I have treated the cat and removed him from the house, but im wondering, can the fleas continue to live and breed if there is no cat for them to feed on? I have emptied two cans of flea spray and powder everywhere, i just the little bloodsuckers to DIE, all of em. Its making me feel really dirty seeing them around. Not seen any since i blitzed the flat with sprays and powders, but can they come back again when theres no cat??