Mopping on Shabbos:
Mopping: It is forbidden to pour water over one’s floor in order to mop it. This applies equally to all floors, even tiled. [This applies even if one does not use a cloth to mop with but rather a plane Squeegee mop. Using a cloth mop, in addition to containing a mopping prohibition as well contains a laundering prohibition.]
It is forbidden to mop one’s floor on Shabbos, even with a squeegee mop.
If liquid spilled on one’s floor may one squeegee the water?
May one remove the drain cover of one’s floor on Shabbos in order to squeegee spilled water into the hole?
If the cover has a handle, or indentation which forms a handle area, then it is permitted to be removed. If there is no handle at all then it is forbidden and is Muktzah.
If water spilled on one’s floor may one place a rag over the water to clean it up?
One may place a designated cloth [i.e. rag] over a spill in order so it absorbs the liquid, whether it is water or other liquid. However one may not wipe the cloth around the floor due to the mopping [and squeezing] prohibition.
May one clean with water a dirty spot on the ground?
Some Poskim rule it is permitted to place water on a dirty area of the floor and then clean the water it in a permitted way [such as to place a rag over the water without moving it around or to squeegee the water].
May one wash and dry one’s counter?
It is permitted to clean one’s counter using water, synthetic cloth and a squeegee. If using a cloth to dry one must beware not to squeeze it in the process.
May one ask a gentile to mop his floor?
With a squeegee: Yes.
With a rag: One may not ask a gentile to use a rag to mop. If one asked a gentile to mop without mentioning any specific way and he decided to use a rag to do so, it is best to protest against the gentile even on a tiled floor. However those which are accustomed to allow the gentile to continue using the rag on a tiled floor without protesting his actions have upon what to rely.
May one polish his floor on Shabbos?
May a hospital mop the floors for hygienic purposes?
Yes. A hospital may be lenient to mop a tiled floor using a squeegee mop [no cloth] for hygienic purposes.
 This prohibition is due to a decree that one may come to smoothen the ditches in the floor, which is a subcategory of the building prohibition. [ibid]
 This applies even in accordance to those opinions which allow sweeping a tiled floor on Shabbos, as mopping does not contain as much of a need as does sweeping. Hence they too agree that by mopping the Sages did not differentiate in their decree between a dirt floor or tiled floor, and they forbade mopping on any of them. [ibid] Thus this prohibition applies even if majority of the city floors are tiled.
 M”B 337/17 [If however the cloth is designated for this purpose, it does not contain a laundering prohibition, but is nevertheless prohibited due to squeezing.]
 In past times oil was poured on a tiled floor in order so one roll over the oil and enter the oil into his skin. Alternatively, it is done in order to shine the floor. In any event it is forbidden to be done for either reason. [Tosefta 17/10]
 As explained in previous footnotes regarding mopping.
Admur adds from the Tosefta that one is not to be “Nofeiach” the floor on Shabbos. Seemingly the meaning of this is that one is not to blow the dust off the floor. Vetzaruch Iyun from Minchas Bikurim on the Tosefta there. See Biur Halacha 337 “Velo Madichin”.
 Lit. Lerabeitz. The above explanation is based on Mishneh Berurah 337/5
 M”B 337/5
 The reason that doing so does not involve a prohibition is because one does not intend to flatten out the gaps [in the ground] but rather to prevent the dust from rising, and it is not inevitable [that one will consequently fill up the gaps in the floor in the process.] [ibid]
 Piskeiy Teshuvos 338/5; SSH”K 23/7
 As since one did not place the water on the floor with intent to mop it, it is therefore permitted to sweep it away. [ibid]
 Piskeiy Teshuvos 308/13; SSH”K 23 footnote 28
 Vetzaruch Iyun as why this is not forbidden being that the cover is attached to the ground and is only removed infrequently. Perhaps however since it is meant for constant removal and insertion it is permitted to be removed, even though one does not constantly remove it.
 Az Nidbaru 1/79-97
 Meaning that the cloth must be designated for cleaning spills. However a regular clothing such as a shirt and the like may not be used due to the laundering prohibition.
 SSH”K 23 footnote 27 in name of Rav SZ”A
 SSH”K 12/40; Piskeiy Teshuvos 338/6
 Kaf Hachayim 337/21
 337/2 regarding sweeping and so seemingly applies for mopping, and so is implied from Kaf Hachayim.
 This is similar to asking a gentile to remove fish from water which is forbidden to be done due to it being a Pesik Reishei. It is not similar to other cases of Pesik Reishei which are permitted to be done through a gentile [see 253/10] as there the Melacha is not being done to the item desired but rather to a different item.
 Admur ibid; SSH”K 23/3
 As in such a case the mopping is as much of a need as is sweeping, and hence the Sages would be lenient. [ibid]