covering

Pluralcoverings

1. 1
   nouncountable

   Something laid over, spread on, or wrapped around another thing to protect, hide, or enclose it.

   A light covering of snow settled over the garden overnight.

   She pulled the protective covering off the new couch.

   Similarlayer, coating, blanket, wrapping, coat

   Note

   A countable noun: it takes a or an, and its plural is coverings. Compounds name the part being covered. Face covering became everyday public-health vocabulary, and Richard Clinnick, writing in May 2020 about advice on using trains, repeats the phrase throughout. Use this sense for the thing itself; for the activity, see the act of covering.

2. 2
   verb

   Present participle of cover.

   Heavy clouds are covering the entire sky this afternoon.

   Volunteers are covering the seedlings to protect them from frost.

   Note

   The -ing form does double duty. As a participle it builds progressive tenses (clouds are covering the sky); as a gerund it names the activity and can stand as subject or object (covering the seedlings took an hour). It goes back to Middle English coveren, also spelled keveren. Most uses are transitive, but the dated intransitive cover, meaning "to put on one's hat," has this form too.

3. 3
   noununcountable

   The act or process of placing something over, onto, or around another thing.

   The covering of the entire stadium roof required several months of work.

   Proper covering of food keeps insects and dust away.

   Similarwrapping

   Note

   The uncountable noun behaves differently from the gerund it resembles. As a noun, it takes the and links to its object with of: the covering of the roof. The gerund, the verb form, takes its object directly: covering the roof. Both name the same action, but only the noun construction accepts adjectives, as in proper covering of food.

4. 4
   nouncountable or uncountable

   In topology, a map between two spaces under which, near each point, the source space looks locally like several separate copies of the target.

   Like a spiral ramp seen from above, where every loop lies over the same circular path.

   The covering maps the real line onto the circle, wrapping it infinitely many times.

   Topologists classify each covering of a space by its fundamental group.

   Note

   Here covering names a map, not a collection of sets. The exact condition is that every point x of X has an open neighborhood U whose preimage under π:E→X splits into disjoint pieces, each carried homeomorphically onto U. Those pieces, indexed by a discrete set, are the "several copies". Keep it apart from the cover by sets, its namesake in the same field. The longer name covering space avoids the clash.

5. 5
   nouncountable or uncountable

   In topology, a collection of sets whose union contains a given set, sometimes required to consist of open sets or of subsets of that set.

   Like tiling a floor with overlapping mats so no spot is left bare.

   The mathematician chose a finite covering of the interval using open sets.

   Every open covering of a compact space has a finite subcollection that still works.

   Note

   Topology uses this one word at three strengths. The loosest is any family of sets whose union contains U. An open covering also requires every member to be open. The strictest version requires every member to lie inside U as well. Writers differ on which is meant, so check the definition in force. Compactness is stated in terms of open coverings.

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