Random word

Explore Metrizable through 10+ example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

Rare word

Metrizable in a sentence

Metrizable meaning

  1. measurable, quantifiable
  2. Of a topological space: for which a metric exists that will induce the original topology.

Using Metrizable

  • The main meaning on this page is: measurable, quantifiable | Of a topological space: for which a metric exists that will induce the original topology.
  • In the example corpus, metrizable often appears in combinations such as: is metrizable, metrizable if, metrizable space.

Context around Metrizable

  • Average sentence length in these examples: 19 words
  • Position in the sentence: 4 start, 9 middle, 7 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

locally 1× completely 1× non 1×

Often after:

space 4× spaces 1× see 1× topological 1×

Sentence patterns with Metrizable

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

every metrizable space is 2× space is metrizable if and 2× but not metrizable in a 1× called a metrizable space see 1× completely metrizable spaces can 1× is always metrizable 1× is locally metrizable but not 1× is non metrizable 1×

Sentence openings and endings

Common sentence openings:

every metrizable space 2× a hausdorff uniform 1× a topological space 1× although the weak 1× completely metrizable spaces 1× examples the group 1×

Common sentence endings:

and second countable 1× compactness using sequences 1× complete metric space 1× essentially the same 1× family of pseudometrics 1× for further details 1×

Words around Metrizable

Just before it in the word index:

metrix 7 metrisable 2 metrics 703 metricon 2 metrication 15 metricated 5

Just after it in the word index:

metrization 2 metro 2.748 metrobank 4 metrobus 5 metrocard 7 metrocards 5

Similar in corpus frequency:

aaj 26 abn 26 aboriginals 26 absalom 26 absolutism 26 abstractly 26

Corpus analysis for Metrizable

  • In this selection, "metrizable" usually appears in the middle of the sentence. The average example has 19 words, and this corpus slice is mostly made up of statements.
  • Around the word, locally, completely, non, space, spaces and see stand out and add context to how "metrizable" is used.
  • Recognizable usage signals include every metrizable space is and space is metrizable if and. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "metrizable" sits close to words such as aaj, abn and aboriginals, which helps place it inside the broader word index.

Example types with metrizable

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

Every metrizable space is first-countable. (6 words)

The weak topology is always metrizable. (6 words)

For example, is not first-countable and thus isn't metrizable. (11 words)

Longer example sentences

Examples The group of unitary operators on a separable Hilbert space endowed with the strong operator topology is metrizable (see Proposition II.1 in Neeb, Karl-Hermann, On a theorem of S. Banach. (33 words)

In fact, general topology tells us that a metrizable space is compact if and only if it is sequentially compact, so that the Bolzano–Weierstrass and Heine–Borel theorems are essentially the same. (33 words)

The superstructure over the real numbers includes a wealth of mathematical structures: For instance, it contains isomorphic copies of all separable metric spaces and metrizable topological vector spaces. (28 words)

Example sentences (20)

The long line is locally metrizable but not metrizable; in a sense it is "too long".

A Hausdorff uniform space is metrizable if its uniformity can be defined by a countable family of pseudometrics.

Although the weak topology of the unit ball is not metrizable in general, one can characterize weak compactness using sequences.

A topological space which can arise in this way from a metric space is called a metrizable space; see the article on metrization theorems for further details.

Completely metrizable spaces can be characterized as those spaces that can be written as an intersection of countably many open subsets of some complete metric space.

Every metrizable space is first-countable.

Every metrizable space is Hausdorff and paracompact (and hence normal and Tychonoff).

Examples The group of unitary operators on a separable Hilbert space endowed with the strong operator topology is metrizable (see Proposition II.1 in Neeb, Karl-Hermann, On a theorem of S. Banach.

Advertentie

For example, a compact Hausdorff space is metrizable if and only if it is second-countable.

For example, is not first-countable and thus isn't metrizable.

If a normed space X is separable, then the weak-* topology is metrizable on the norm-bounded subsets of X*.

If the dual X ′ is separable, the weak topology of the unit ball of X is metrizable.

In fact, general topology tells us that a metrizable space is compact if and only if it is sequentially compact, so that the Bolzano–Weierstrass and Heine–Borel theorems are essentially the same.

It states that a topological space is metrizable if and only if it is regular, Hausdorff and has a σ-locally finite base.

The real line with the lower limit topology is not metrizable.

The superstructure over the real numbers includes a wealth of mathematical structures: For instance, it contains isomorphic copies of all separable metric spaces and metrizable topological vector spaces.

The weak topology is always metrizable.

This is not true in general if Y is non-metrizable.

Urysohn's Theorem can be restated as: A topological space is separable and metrizable if and only if it is regular, Hausdorff and second-countable.

What Urysohn had shown, in a paper published posthumously in 1925, was that every second-countable normal Hausdorff space is metrizable).

Advertentie

Common combinations with metrizable

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "metrizable" in a sentence?
An example: "The long line is locally metrizable but not metrizable; in a sense it is "too long"." This page contains 10+ example sentences with the word "metrizable" from authentic English texts.
What does "metrizable" mean?
Metrizable means: measurable, quantifiable
How many example sentences with "metrizable" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "metrizable", drawn from a database of millions of English sentences.