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closed

closed

7.5
A range of numbers that includes both end points
  • adjective
  • /kloʊzd/
  • Specialized
translation icon : cerrado
  • A closed interval includes both endpoints, making it vital for certain mathematical proofs.

Examples

  • Then the closed unit ball is not compact.

  • It's the smallest closed set that contains your smaller set, right?

  • So H is closed under the group operation.

  • Now what about a theory of closed strings that AB initio starts with closed strings?

  • I'll spoke can't on the closed interval a comma B OK.

  • The closed set, which contains all points of the interval, is essential in topology.

  • For the function to be defined over the closed range, both endpoints must be included.

Antonyms

open interval
  • Specialized
8.2

A set of numbers between two points that does not include the end points

Idioms

behind closed doors
  • Literature
112 4.1

In private and not open to the public

To keep quiet to avoid saying something silly

with eyes closed
  • Informal
4.9

To do something easily without thinking because you trust or know it well

Compounds

19 5.3

Not open to the public and held privately by a small group

15 4.2

A private meeting or place that people keep secret

14 4.1

A space surrounded on all sides and not open to the outside

8 5.5

A part of a meeting that is not open to the public

closed-circuit
  • Specialized
5 5.3

A system that keeps video or sound inside a private network

4 6.4

A workplace that only hires people who belong to a union

A system of cameras and monitors that records and shows images for security, not for public broadcast

2 7.2

An election to choose a party candidate in which only registered members of the party can vote

closed circuit
  • Specialized
2 4.3

A complete path that lets electricity or signals flow

closed loop
  • Specialized
1 5.1

A system that uses feedback to keep things like temperature at the right level

Includes captions that viewers can turn on to read the dialogue

closed book
  • Informal
1 7.4

Something that is hard to understand or know much about

closed fracture
  • Specialized
1 4.1

A broken bone that does not break the skin

closed universe
  • Specialized
1 9.9

A model of the universe whose space curves and contains enough matter to stop and reverse its expansion

closed-end fund
  • Specialized
1 7.2

A company that sells a set number of shares that trade on the stock market

closed curve
  • Specialized
6.5

A curve with no endpoints that comes back to its starting point, like a circle

A plant with blue or purple flowers shaped like a tube that stay mostly closed

closed interval
  • Specialized
7.3

All numbers from one number to another including both ends

closed syllable
  • Specialized
6.0

A syllable that ends with a consonant and has a short vowel sound

closed-angle glaucoma
  • Specialized
6.7

A sudden eye condition when the colored part blocks fluid leaving the front of the eye, raising eye pressure quickly

closed-class word
  • Specialized
8.3

A word from a small fixed set that helps show grammar, like in or and

A company that issues a fixed number of shares which are traded on a stock market

closed chain
  • Specialized
6.9

A ring of atoms joined in a molecule to form a loop

closed corporation
  • Specialized
7.0

A company whose shares are owned by a small group and not sold to the public

closed couplet
  • Literature
7.9

Two lines of poetry that rhyme and give a complete thought

closed-heart surgery
  • Specialized
6.1

Heart surgery done through a small cut without opening the chest

closed-loop system
  • Specialized
6.0

A control system that uses information from sensors to adjust itself automatically

closed-loop system
  • Specialized
5.2

A system that recovers, cleans, and reuses materials to avoid waste

closed-ring
  • Specialized
7.7

Having atoms joined together to form a ring

simple closed curve
  • Specialized
7.9

A curved line on a flat surface that makes a closed loop without crossing itself, like a circle

How Open-ended

limitless
41 4.0
unrestricted
24 4.1
open-ended
27 4.9
closed
  • Specialized
7.5
fixed
1.8
limited
393 2.5

Surface Forms

closed positive

Morphology

closed = close (opaque) = close + ed

The mathematical sense 'containing both endpoints' is a technicalized meaning; knowing the verb 'close' does not make this precise definition obvious to average learners.

Etymology

In math, a closed interval contains its end points, and the name comes from the old Latin claudere meaning 'to shut', so the ends are 'shut in' or included.