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Get to know Isometry better with 10+ real example sentences, the meaning and synonyms like mapping or map.

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Isometry in a sentence

Isometry meaning

A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their preimages.

Synonyms of Isometry

growth rate rate of growth mapping map correspondence elevation equality

Related words

Other words often associated with Isometry or its synonyms:

function rate agreement height sameness ascent meridian status explore raising pinnacle equivalence

Using Isometry

  • The main meaning on this page is: A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their preimages.
  • Useful related words include: growth rate, rate of growth, mapping, map.
  • In the example corpus, isometry often appears in combinations such as: an isometry, isometry is, isometry between.

Context around Isometry

  • Average sentence length in these examples: 19.8 words
  • Position in the sentence: 4 start, 5 middle, 3 end
  • Sentence types: 12 statements, 0 questions, 0 exclamations

Often before:

surjective 1× quasi 1× tree 1× discrete 1×

Often after:

groups 2× symmetry 1× classes 1×

Sentence patterns with Isometry

These short patterns come directly from the example sentences and show how the word is often embedded:

4 tree isometry was described 1× a quasi isometry is not 1× a surjective isometry between the 1× all discrete isometry groups and 1× are more isometry groups than 1× becomes an isometry 1× containing this isometry symmetry type 1× except the isometry between the 1×

Sentence openings and endings

Common sentence openings:

a surjective isometry 1× an object without 1× if we further 1× isometries the map 1× note that a 1× the corresponding map 1×

Common sentence endings:

1978 by sedgewick 1× a rational number 1× abstract group type 1× becomes an isometry 1× between the simplexes 1× called isometrically isomorphic 1×

Words around Isometry

Just before it in the word index:

isometries 9 isometrically 8 isometric 49 isomers 79 isomerized 3 isomerization 9

Just after it in the word index:

isomorphic 122 isomorphism 111 isomorphisms 21 isomorphous 6 ison 13 isong 6

Similar in corpus frequency:

aami 15 aat 15 abada 15 abcs 15 abdulkareem 15 abha 15

Corpus analysis for Isometry

  • In this selection, "isometry" usually appears in the middle of the sentence. The average example has 19.8 words, and this corpus slice is mostly made up of statements.
  • Around the word, surjective, quasi, tree, groups, symmetry and classes stand out and add context to how "isometry" is used.
  • Recognizable usage signals include 4 tree isometry was described and a quasi isometry is not. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "isometry" sits close to words such as aami, aat and abada, which helps place it inside the broader word index.

Example types with isometry

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

Note that a quasi-isometry is not required to be continuous. (11 words)

The 2-4 tree isometry was described in 1978 by Sedgewick. (11 words)

The corresponding map is an isometry but in general not onto. (11 words)

Longer example sentences

With 2-4 trees, the isometry is resolved by a "color flip," corresponding to a split, in which the red color of two children nodes leaves the children and moves to the parent node. (34 words)

Isometries The map f:M 1 →M 2 is an isometry if : Isometries are always injective ; the image of a compact or complete set under an isometry is compact or complete, respectively. (32 words)

This includes all discrete isometry groups and also those involved in continuous symmetries, but excludes for example in 1D the group of translations by a rational number. (27 words)

Example sentences (12)

Isometries The map f:M 1 →M 2 is an isometry if : Isometries are always injective ; the image of a compact or complete set under an isometry is compact or complete, respectively.

An object without any symmetry has as symmetry group the trivial group only containing this isometry (symmetry type C 1 ).

A surjective isometry between the normed vector spaces V and W is called an isometric isomorphism, and V and W are called isometrically isomorphic.

If we further consider both spaces with the sup norm the extension map becomes an isometry.

Note that a quasi-isometry is not required to be continuous.

The 2-4 tree isometry was described in 1978 by Sedgewick.

The corresponding map is an isometry but in general not onto.

There are more isometry groups than these two, of the same abstract group type.

Advertentie

The same arguments are also valid for a general parallelotope, except the isometry between the simplexes.

This includes all discrete isometry groups and also those involved in continuous symmetries, but excludes for example in 1D the group of translations by a rational number.

Using this distance, the class of all (isometry classes of) compact metric spaces becomes a metric space in its own right.

With 2-4 trees, the isometry is resolved by a "color flip," corresponding to a split, in which the red color of two children nodes leaves the children and moves to the parent node.

Advertentie

Common combinations with isometry

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "isometry" in a sentence?
An example: "Isometries The map f:M 1 →M 2 is an isometry if : Isometries are always injective ; the image of a compact or complete set under an isometry is compact or complete, respectively." This page contains 10+ example sentences with the word "isometry" from authentic English texts.
What does "isometry" mean?
Isometry means: A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their preimages.
What are synonyms of "isometry"?
Common synonyms of "isometry" include: growth rate, rate of growth, mapping, map, correspondence, elevation, equality.
How many example sentences with "isometry" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "isometry", drawn from a database of millions of English sentences.