We have some natural stone tile which is pretty coarse. This is actually a very pretty (IMO) natural texture but it is a little hard to clean. Vacuuming is fine but like most hard surfaces also needs some wet cleaning from time to time.
Regular mops we've tried tend to fall apart and leave bits behind on this surface. Sponge or cloth string types. Maybe there is something we haven't tried or thought of... or maybe there is a certain type of cleaner or something other than mopping that would help?
Just to be clear, I'm not asking for advise on leveling the floor or smoothing it, since that's not something we perceive as a problem itself.