You guys peaked my curiosity about cement floors since I had never heard of them before.......I have to say they are gorgeous! So as I am reading this I want to add some "mop" info that might help
O-Cedar - Products - Systems - Systems - UltraMax™ All-In-One Mopping Kit
This is the mop that I have been using and I love it! As I'm sure you know from my fall I have laminate floor but they too are hard to keep clean and I hated the streaks from the bazillionth mops that I had purchased in the past. This one is microfiber and is washable and dryable. It is by far the very best mop that I have ever owned! I bought it at Walmart about 7 or 8 months ago with 3 extra mop pad thingies and after I mop I just toss it into the washer and then into the dryer and they look like new still. Love it!