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On this page you'll find 10+ example sentences with Preregular. Discover the meaning, how to use the word correctly in a sentence.

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Preregular in a sentence

Related words

Preregular | Preregularity

Preregular meaning

In which any two topologically distinguishable points can be separated by neighbourhoods

Using Preregular

  • The main meaning on this page is: In which any two topologically distinguishable points can be separated by neighbourhoods
  • In the example corpus, preregular often appears in combinations such as: preregular spaces, of preregular, is preregular.

Context around Preregular

  • Average sentence length in these examples: 24.2 words
  • Position in the sentence: 0 start, 4 middle, 7 end
  • Sentence types: 11 statements, 0 questions, 0 exclamations

Often before:

non 1×

Often after:

spaces 4× space 1× cannot 1×

Sentence patterns with Preregular

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

space is preregular 2× are always preregular so the 1× at least preregular and then 1× for all preregular spaces they 1× hence not preregular cannot be 1× idea of preregular spaces came 1× indistinguishability for preregular spaces 1× is both preregular i e 1×

Sentence openings and endings

Common sentence openings:

although hausdorff spaces 2× a related but 1× a topological space 1× as described above 1× as it turns 1× indeed when analysts 1×

Common sentence endings:

space is preregular 2× a preregular space 1× are topologically distinguishable 1× cannot be regular 1× for preregular spaces 1× non preregular spaces 1×

Words around Preregular

Just before it in the word index:

preregistration 5 preregistered 4 preregister 2 prerecorded 40 prerana 4 prequels 80

Just after it in the word index:

preregularity 4 prerelease 6 prerenal 3 prerequisite 163 prerequisites 68 prerna 14

Similar in corpus frequency:

aadi 14 aayush 14 abbottabad 14 aberdonian 14 abhi 14 aborting 14

Corpus analysis for Preregular

  • In this selection, "preregular" usually appears near the end of the sentence. The average example has 24.2 words, and this corpus slice is mostly made up of statements.
  • Around the word, non, spaces, space and cannot stand out and add context to how "preregular" is used.
  • Recognizable usage signals include space is preregular and are always preregular so the. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "preregular" sits close to words such as aadi, aayush and abbottabad, which helps place it inside the broader word index.

Example types with preregular

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

A related, but weaker, notion is that of a preregular space. (11 words)

The related concept of Scott domain also consists of non-preregular spaces. (12 words)

There are other common definitions: They are all equivalent if X is a Hausdorff space (or preregular). (17 words)

Longer example sentences

The characteristic that unites the concept in all of these examples is that limits of nets and filters (when they exist) are unique (for separated spaces) or unique up to topological indistinguishability (for preregular spaces). (35 words)

A topological space is Hausdorff if and only if it is both preregular (i.e. topologically distinguishable points are separated by neighbourhoods) and Kolmogorov (i.e. distinct points are topologically distinguishable). (31 words)

Indeed, when analysts run across a non-Hausdorff space, it is still probably at least preregular, and then they simply replace it with its Kolmogorov quotient, which is Hausdorff. (29 words)

Example sentences (11)

Most of the time, these results hold for all preregular spaces; they were listed for regular and Hausdorff spaces separately because the idea of preregular spaces came later.

Although Hausdorff spaces are not, in general, regular, a Hausdorff space that is also (say) locally compact will be regular, because any Hausdorff space is preregular.

Although Hausdorff spaces aren't generally regular, a Hausdorff space that is also (say) locally compact will be regular, because any Hausdorff space is preregular.

A related, but weaker, notion is that of a preregular space.

As described above, any completely regular space is regular, and any T 0 space that is not Hausdorff (and hence not preregular) cannot be regular.

As it turns out, uniform spaces, and more generally Cauchy spaces, are always preregular, so the Hausdorff condition in these cases reduces to the T 0 condition.

A topological space is Hausdorff if and only if it is both preregular (i.e. topologically distinguishable points are separated by neighbourhoods) and Kolmogorov (i.e. distinct points are topologically distinguishable).

Indeed, when analysts run across a non-Hausdorff space, it is still probably at least preregular, and then they simply replace it with its Kolmogorov quotient, which is Hausdorff.

The characteristic that unites the concept in all of these examples is that limits of nets and filters (when they exist) are unique (for separated spaces) or unique up to topological indistinguishability (for preregular spaces).

There are other common definitions: They are all equivalent if X is a Hausdorff space (or preregular).

The related concept of Scott domain also consists of non-preregular spaces.

Common combinations with preregular

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "preregular" in a sentence?
An example: "Most of the time, these results hold for all preregular spaces; they were listed for regular and Hausdorff spaces separately because the idea of preregular spaces came later." This page contains 10+ example sentences with the word "preregular" from authentic English texts.
What does "preregular" mean?
Preregular means: In which any two topologically distinguishable points can be separated by neighbourhoods
How many example sentences with "preregular" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "preregular", drawn from a database of millions of English sentences.