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How do you use Kuratowski in a sentence? See 10+ example sentences showing how this word appears in different contexts.

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Kuratowski in a sentence

Using Kuratowski

  • In the example corpus, kuratowski often appears in combinations such as: kuratowski subgraph, kuratowski was, the kuratowski.

Context around Kuratowski

  • Average sentence length in these examples: 15.7 words
  • Position in the sentence: 11 start, 8 middle, 1 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

proving 1× notation 1× 1921 1× furthermore 1× 1945 1× kazimierz 1× use 1×

Often after:

subgraph 2× closure 2× proved 1× zorn 1× implemented 1× worked 1× pairs 1× finiteness 1× started 1× stated 1×

Sentence patterns with Kuratowski

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

41 p kuratowski implemented many 1× as the kuratowski closure axioms 1× autumn 1921 kuratowski was awarded 1× contain a kuratowski subgraph 1× february 1945 kuratowski started to 1× fulfilled the kuratowski closure axioms 1× furthermore kuratowski worked as 1× have a kuratowski subgraph 1×

Sentence openings and endings

Common sentence openings:

a year later 1× after world war 1× bulletin of the 1× doctoral thesis in 1× furthermore kuratowski worked 1× he implemented the 1×

Common sentence endings:

a kuratowski subgraph 2× 1980 in warsaw 1× a finite set 1× are proper classes 1× awarded the ph 1× axiom of idempotence 1×

Words around Kuratowski

Just before it in the word index:

kurata 5 kurashiki 4 kurashev 7 kurash 3 kuras 5 kuraray 2

Just after it in the word index:

kurauone 2 kurbanov 2 kurbatova 2 kurbegovic 2 kurbis 3 kurchatov 3

Similar in corpus frequency:

abdulkadir 36 abed 36 abhay 36 abimbola 36 abiotic 36 abkhazia 36

Corpus analysis for Kuratowski

  • In this selection, "kuratowski" usually appears near the start of the sentence. The average example has 15.7 words, and this corpus slice is mostly made up of statements.
  • Around the word, proving, notation, 1921, subgraph, closure and proved stand out and add context to how "kuratowski" is used.
  • Recognizable usage signals include 41 p kuratowski implemented many and as the kuratowski closure axioms. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "kuratowski" sits close to words such as abdulkadir, abed and abhay, which helps place it inside the broader word index.

Example types with kuratowski

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

Kuratowski died on 18 June 1980 in Warsaw. (8 words)

Kuratowski was also dean of the department twice. (8 words)

Doctoral thesis In autumn 1921 Kuratowski was awarded the Ph. (10 words)

Longer example sentences

He then redefined the pair : where the component Cartesian products are Kuratowski pairs of sets and where : This renders possible pairs whose projections are proper classes. (26 words)

With this notation, Kuratowski's theorem can be expressed succinctly: a graph is planar if and only if it does not have a Kuratowski subgraph. (25 words)

The more difficult direction in proving Kuratowski's theorem is to show that, if a graph is nonplanar, it must contain a Kuratowski subgraph. (24 words)

Example sentences (20)

Kuratowski proved the Kuratowski-Zorn lemma (often called just Zorn's lemma ) in 1922.

The more difficult direction in proving Kuratowski's theorem is to show that, if a graph is nonplanar, it must contain a Kuratowski subgraph.

With this notation, Kuratowski's theorem can be expressed succinctly: a graph is planar if and only if it does not have a Kuratowski subgraph.

After World War II, Kuratowski was actively involved in the rebuilding of scientific life in Poland.

A year later Kuratowski was nominated as the head of Mathematics Department there.

Bulletin of the American Mathematical Society, 41: p. Kuratowski implemented many concepts in set theory and topology.

Doctoral thesis In autumn 1921 Kuratowski was awarded the Ph.

Furthermore, Kuratowski worked as an editor in the Polish Academy of Sciences Bulletin.

Advertentie

He implemented the closure axioms (known in mathematical circles as the Kuratowski closure axioms ).

Here Hausdorff discussed spaces which fulfilled the Kuratowski closure axioms up to just the axiom of idempotence.

He then redefined the pair : where the component Cartesian products are Kuratowski pairs of sets and where : This renders possible pairs whose projections are proper classes.

However, Kuratowski finiteness would fail for the same set of socks.

In February 1945, Kuratowski started to lecture at the reopened Warsaw University.

Kazimierz Kuratowski stated in 1930 that K 3,3 is nonplanar, citation.

Kuratowski died on 18 June 1980 in Warsaw.

Kuratowski finite means S lies in the set K(S), constructed as follows.

Kuratowski left Lwów for Warsaw in 1934, before the famous Scottish Book was begun (in 1935), hence did not contribute any problems to it.

Kuratowski showed that this is equivalent to the numerical definition of a finite set.

Kuratowski was also dean of the department twice.

Other planarity criteria In practice, it is difficult to use Kuratowski's criterion to quickly decide whether a given graph is planar.

Advertentie

Common combinations with kuratowski

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "kuratowski" in a sentence?
An example: "Kuratowski proved the Kuratowski-Zorn lemma (often called just Zorn's lemma ) in 1922." This page contains 10+ example sentences with the word "kuratowski" from authentic English texts.
How many example sentences with "kuratowski" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "kuratowski", drawn from a database of millions of English sentences.