On this page you'll find 10+ example sentences with Homeomorphism. Discover the meaning, how to use the word correctly in a sentence.
Homeomorphism meaning
- a continuous bijection from one topological space to another, with continuous inverse.
- a similarity in the crystal structure of unrelated compounds
Using Homeomorphism
- The main meaning on this page is: a continuous bijection from one topological space to another, with continuous inverse. | a similarity in the crystal structure of unrelated compounds
- In the example corpus, homeomorphism often appears in combinations such as: is homeomorphism, homeomorphism is, homeomorphism between.
Context around Homeomorphism
- Average sentence length in these examples: 20 words
- Position in the sentence: 3 start, 11 middle, 6 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Homeomorphism
- In this selection, "homeomorphism" usually appears in the middle of the sentence. The average example has 20 words, and this corpus slice is mostly made up of statements.
- Around the word, self, explicit, corresponding, classes and onto stand out and add context to how "homeomorphism" is used.
- Recognizable usage signals include a homeomorphism is a and a self homeomorphism is a. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "homeomorphism" sits close to words such as aare, aarti and abl, which helps place it inside the broader word index.
Example types with homeomorphism
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
From this need arises the notion of homeomorphism. (8 words)
The resulting equivalence classes are called homeomorphism classes. (8 words)
Homeomorphism can be considered the most basic topological equivalence. (9 words)
Some authors add the assumption that the starting space X be Tychonoff (or even locally compact Hausdorff), for the following reasons: *The map from X to its image in βX is a homeomorphism if and only if X is Tychonoff. (40 words)
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)
Extensions of diffeomorphisms In 1926, Tibor Radó asked whether the harmonic extension of any homeomorphism or diffeomorphism of the unit circle to the unit disc yields a diffeomorphism on the open disc. (32 words)
Example sentences (20)
A self-homeomorphism is a homeomorphism of a topological space and itself.
Every diffeomorphism is a homeomorphism, but not every homeomorphism is a diffeomorphism.
Homotopy equivalence is a rougher relationship than homeomorphism; a homotopy equivalence class can contain several homeomorphism classes.
A homeomorphism is a bijection that is continuous and whose inverse is also continuous.
An embedding, or a smooth embedding, is defined to be an injective immersion which is an embedding in the topological sense mentioned above (i.e. homeomorphism onto its image).
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.
An introductory exercise is to classify the uppercase letters of the English alphabet according to homeomorphism and homotopy equivalence.
Extensions of diffeomorphisms In 1926, Tibor Radó asked whether the harmonic extension of any homeomorphism or diffeomorphism of the unit circle to the unit disc yields a diffeomorphism on the open disc.
From this need arises the notion of homeomorphism.
Furthermore, ι 1 is also continuous, so ι is a homeomorphism.
Homeomorphism can be considered the most basic topological equivalence.
If X is a Tychonoff space then the map from X to its image in βX is a homeomorphism, so X can be thought of as a (dense) subspace of βX.
In 1930 in Erweiterung einer Homöomorphie (extending a homeomorphism) he showed the following: Let be a metric space, a closed subset.
In the algebraic approach, one finds a correspondence between spaces and groups that respects the relation of homeomorphism (or more general homotopy ) of spaces.
More explicitly, an injective continuous map between topological spaces and is a topological embedding if yields a homeomorphism between and (where carries the subspace topology inherited from ).
Recall that the stereographic projection S gives an explicit homeomorphism from the unit sphere minus the north pole (0,0,1) to the Euclidean plane.
Some authors add the assumption that the starting space X be Tychonoff (or even locally compact Hausdorff), for the following reasons: *The map from X to its image in βX is a homeomorphism if and only if X is Tychonoff.
Such a neighborhood, together with the corresponding homeomorphism, is known as a (coordinate) chart.
Technical terms such as homeomorphism and integrable have precise meanings in mathematics.
The resulting equivalence classes are called homeomorphism classes.
Common combinations with homeomorphism
These word pairs occur most frequently in English texts:
- is homeomorphism 5×
- homeomorphism is 3×
- homeomorphism between 3×
- than homeomorphism 2×
- homeomorphism classes 2×
- to homeomorphism 2×
- homeomorphism and 2×
- homeomorphism or 2×
- of homeomorphism 2×