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

Rare word

Homeomorphic in a sentence

Homeomorphic meaning

Having a homeomorphism

Using Homeomorphic

  • The main meaning on this page is: Having a homeomorphism
  • In the example corpus, homeomorphic often appears in combinations such as: homeomorphic to, is homeomorphic, not homeomorphic.

Context around Homeomorphic

  • Average sentence length in these examples: 20.9 words
  • Position in the sentence: 2 start, 9 middle, 9 end
  • Sentence types: 18 statements, 2 questions, 0 exclamations

Often before:

bridges 1× space 1× necessarily 1× sphere 1× manifold 1× particular 1×

Often after:

image 1× smooth 1× copy 1× spaces 1×

Sentence patterns with Homeomorphic

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

is not homeomorphic to the 2× any space homeomorphic to a 1× are not homeomorphic because removing 1× are not homeomorphic to the 1× contain a homeomorphic copy of 1× containing a homeomorphic image of 1× four manifold homeomorphic to the 1× i e homeomorphic to a 1×

Sentence openings and endings

Common sentence openings:

a torus is 1× an equivalent form 1× but the circle 1× elements of are 1× for dimensions greater 1× for example a 1×

Common sentence endings:

the sierpinski carpet 2× to a sphere 2× 3 dimensional sphere 1× cutting or gluing 1× even locally compact 1× homeomorphic to it 1×

Words around Homeomorphic

Just before it in the word index:

homeodomain 5 homeobox 5 homeniuk 2 homenewsweek 2 homenetmen 5 homendy 10

Just after it in the word index:

homeomorphism 24 homeomorphisms 5 homeopath 3 homeopathic 35 homeopaths 11 homeopathy 48

Similar in corpus frequency:

abaribe 42 abbasids 42 abstentions 42 abundances 42 acadians 42 acrisure 42

Corpus analysis for Homeomorphic

  • In this selection, "homeomorphic" usually appears in the middle of the sentence. The average example has 20.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, bridges, space, necessarily, image, smooth and copy stand out and add context to how "homeomorphic" is used.
  • Recognizable usage signals include is not homeomorphic to the and any space homeomorphic to a. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "homeomorphic" sits close to words such as abaribe, abbasids and abstentions, which helps place it inside the broader word index.

Example types with homeomorphic

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 torus is not homeomorphic to a sphere. (8 words)

In particular, homeomorphic spaces have isomorphic Alexandroff extensions. (8 words)

But the circle is not homeomorphic to the doughnut. (9 words)

Longer example sentences

An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence : if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it. (35 words)

For example, X and Y are not homeomorphic because removing the center point of the X leaves four pieces; whatever point in Y corresponds to this point, its removal can leave at most three pieces. (35 words)

The impossibility of crossing each bridge just once applies to any arrangement of bridges homeomorphic to those in Königsberg, and the hairy ball theorem applies to any space homeomorphic to a sphere. (32 words)

Question examples

For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere? (22 words)

Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere? (23 words)

Example sentences (20)

The impossibility of crossing each bridge just once applies to any arrangement of bridges homeomorphic to those in Königsberg, and the hairy ball theorem applies to any space homeomorphic to a sphere.

An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence : if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.

A torus is not homeomorphic to a sphere.

But the circle is not homeomorphic to the doughnut.

Elements of are sometimes called reals as well and though containing a homeomorphic image of in addition to being totally disconnected isn't even locally compact.

For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n-sphere homeomorphic to the n-sphere?

For example, a Dehn filling with slope on any knot in the 3-sphere gives a homology sphere; typically these are not homeomorphic to the 3-sphere.

For example, X and Y are not homeomorphic because removing the center point of the X leaves four pieces; whatever point in Y corresponds to this point, its removal can leave at most three pieces.

Advertentie

Freedman's work left open the possibility that there is a smooth four-manifold homeomorphic to the four-sphere which is not diffeomorphic to the four-sphere.

However, by the results of Whyburn mentioned above, we can see that the Wallis sieve is homeomorphic to the Sierpinski carpet.

However, in 1958 Gordon Whyburn citation uniquely characterized the Sierpinski carpet as follows: any curve that is locally connected and has no 'local cut-points' is homeomorphic to the Sierpinski carpet.

However, it has a subgraph that is homeomorphic to K 3,3 and is therefore not planar.

However, the underlying topological spaces within the Möbius strip are homeomorphic in each case.

If such a function exists, we say X and Y are homeomorphic.

In dimensions 1, 2, 3, any pair of homeomorphic smooth manifolds are diffeomorphic.

In general, a surface is said to be orientable if it does not contain a homeomorphic copy of the Möbius strip; intuitively, it has two distinct "sides".

In particular, homeomorphic spaces have isomorphic Alexandroff extensions.

Intuitively, two spaces are homeomorphic if one can be deformed into the other without cutting or gluing.

Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?

Its boundary is a simple closed curve, i.e., homeomorphic to a circle.

Advertentie

Common combinations with homeomorphic

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "homeomorphic" in a sentence?
An example: "The impossibility of crossing each bridge just once applies to any arrangement of bridges homeomorphic to those in Königsberg, and the hairy ball theorem applies to any space homeomorphic to a sphere." This page contains 10+ example sentences with the word "homeomorphic" from authentic English texts.
What does "homeomorphic" mean?
Homeomorphic means: Having a homeomorphism
How many example sentences with "homeomorphic" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "homeomorphic", drawn from a database of millions of English sentences.