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covering

From Wiktionary, the free dictionary

English

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EnglishWikipedia has an article on:
Wikipedia

Pronunciation

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Etymology 1

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Present participle orparticipial adjective fromcover(verb) +‎-ing; or, fromMiddle English participle form ofcoveren,keveren(“to cover”).

Verb

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covering

  1. presentparticiple andgerund ofcover

Etymology 2

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FromMiddle Englishcoverynge,-inge,keverynge,-inge [verbal noun ofcoveren,keveren(“to cover”)];[1] or, verbal noun fromcover(verb) +‎-ing.

Noun

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covering (countable anduncountable,pluralcoverings)

  1. (countable) That whichcovers orconceals; acover; somethingspread orlaid over orwrapped about another.
    • 2020 May 20, Richard Clinnick, “Network News: More trains... but advice is not to use public transport”, inRail, page 6:
      Facecovering is also mentioned: "There are some circumstances when wearing a facecovering may be marginally beneficial as a precautionary measure. The evidence suggests that wearing a facecovering does not protect you, but it may protect others if you are infected but have not yet developed symptoms. [...] If you can, wear a facecovering if you need to use public transport."
  2. (uncountable) Action of the verbtocover.
  3. (topology, of a givenopen setU{\displaystyle U}) Acollection of sets{Ui}{\displaystyle \{U_{i}\}} such that theirunion containsU{\displaystyle U}; such a collection with the additional property that everyUi{\displaystyle U_{i}} is open; such a collection with the additional property that everyUi{\displaystyle U_{i}} is contained inU{\displaystyle U}.
  5. (topology) A special kind ofmap that establishes a relationship between twotopological spaces in the sense that, under theaction of the map, the one lookslocally like several copies of the second: Formally, acontinuousmapπ:E→X{\displaystyle \pi :E\rightarrow X} betweentopological spaces such that there exists, for every pointx{\displaystyle x} inX{\displaystyle X}, adiscretespaceDx{\displaystyle D_{x}} and anopenneighborhoodU{\displaystyle U} ofx{\displaystyle x} such thatπ−1(U)=⨆d∈DxVd{\displaystyle \pi ^{-1}(U)=\displaystyle \bigsqcup _{d\in D_{x}}V_{d}} andπ|Vd:Vd→U{\displaystyle \pi |_{V_{d}}:V_{d}\rightarrow U} is ahomeomorphism for everyd∈Dx{\displaystyle d\in D_{x}}. SeeCovering space on Wikipedia.Wikipedia
Usage notes
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In sensesense 4, properly, the mapπ{\displaystyle \pi } is the covering, andE{\displaystyle E} is called thecovering space, but byabuse of terminology, "covering" may refer toE{\displaystyle E}, "covering space" may refer toπ{\displaystyle \pi }, and either may refer to thetuple(E,π){\displaystyle (E,\pi )}.

Derived terms
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Translations
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that which covers something

References

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  1. ^“cǒveringe,ger.(1).”, inMED Online, Ann Arbor, Mich.:University of Michigan,2018, retrieved16 December 2019.
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