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How do you use Pseudometric in a sentence? See 8 example sentences showing how this word appears in different contexts, plus the exact meaning.

Rare word

Pseudometric in a sentence

Related words

Pseudometric | Pseudometrics

Pseudometric meaning

Describing a generalization of a metric space in which the distance between two distinct points can be zero.

Using Pseudometric

  • The main meaning on this page is: Describing a generalization of a metric space in which the distance between two distinct points can be zero.
  • In the example corpus, pseudometric often appears in combinations such as: pseudometric space, the pseudometric, is pseudometric.

Context around Pseudometric

  • Average sentence length in these examples: 20.4 words
  • Position in the sentence: 0 start, 7 middle, 1 end
  • Sentence types: 8 statements, 0 questions, 0 exclamations

Often before:

single 2× complete 1×

Often after:

space 3× definition 1×

Sentence patterns with Pseudometric

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

a complete pseudometric space is 1× a single pseudometric 1× a single pseudometric which is 1× fortiori a pseudometric the pseudometric 1× hence the pseudometric as defined 1× in a pseudometric space may 1× is a pseudometric 1× is a pseudometric on m 1×

Sentence openings and endings

Common sentence openings:

indeed as discussed 1× indeed since a 1× less trivially it 1× note that the 1× other examples include 1× proof the following 1×

Common sentence endings:

a baire space 1× a single pseudometric 1× a true metric 1× a uniform structure 1× is a pseudometric 1× is completely regular 1×

Words around Pseudometric

Just before it in the word index:

pseudomembrane 2 pseudolus 10 pseudokinase 2 pseudohermaphroditism 2 pseudogenes 3 pseudogene 2

Just after it in the word index:

pseudometrics 3 pseudomonas 15 pseudomorph 2 pseudonana 2 pseudonormal 2 pseudonym 230

Similar in corpus frequency:

aargau 11 abacos 11 abboud 11 abbreviate 11 abdelkader 11 abdomens 11

Corpus analysis for Pseudometric

  • In this selection, "pseudometric" usually appears in the middle of the sentence. The average example has 20.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, single, complete, space and definition stand out and add context to how "pseudometric" is used.
  • Recognizable usage signals include a complete pseudometric space is and a single pseudometric. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "pseudometric" sits close to words such as aargau, abacos and abboud, which helps place it inside the broader word index.

Example types with pseudometric

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

The function d is a pseudometric on M. Every metric is a pseudometric. (13 words)

Other examples include: * Every metric space is Tychonoff; every pseudometric space is completely regular. (14 words)

That is, points in a pseudometric space may be "infinitely close" without being identical. (14 words)

Longer example sentences

Less trivially, it can be shown that a uniform structure that admits a countable fundamental system of entourages (and hence in particular a uniformity defined by a countable family of pseudometrics) can be defined by a single pseudometric. (38 words)

Note that the symmetric difference of two distinct sets can have measure zero; hence the pseudometric as defined above need not to be a true metric. (26 words)

Indeed, as discussed above, such a uniformity can be defined by a single pseudometric, which is necessarily a metric if the space is Hausdorff. (24 words)

Example sentences (8)

Indeed, since a metric is a fortiori a pseudometric, the pseudometric definition furnishes M with a uniform structure.

The function d is a pseudometric on M. Every metric is a pseudometric.

Indeed, as discussed above, such a uniformity can be defined by a single pseudometric, which is necessarily a metric if the space is Hausdorff.

Less trivially, it can be shown that a uniform structure that admits a countable fundamental system of entourages (and hence in particular a uniformity defined by a countable family of pseudometrics) can be defined by a single pseudometric.

Note that the symmetric difference of two distinct sets can have measure zero; hence the pseudometric as defined above need not to be a true metric.

Other examples include: * Every metric space is Tychonoff; every pseudometric space is completely regular.

Proof The following is a standard proof that a complete pseudometric space is a Baire space.

That is, points in a pseudometric space may be "infinitely close" without being identical.

Common combinations with pseudometric

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "pseudometric" in a sentence?
An example: "Indeed, since a metric is a fortiori a pseudometric, the pseudometric definition furnishes M with a uniform structure." This page contains 8 example sentences with the word "pseudometric" from authentic English texts.
What does "pseudometric" mean?
Pseudometric means: Describing a generalization of a metric space in which the distance between two distinct points can be zero.
How many example sentences with "pseudometric" are there?
Voorbeeldzinnen.info contains 8 example sentences with "pseudometric", drawn from a database of millions of English sentences.