Below you will find example sentences with "simply connected". The examples show how this phrase is used in natural context and which words often surround it.

Simply Connected in a sentence

Corpus data

  • Displayed example sentences: 16
  • Discovered as a combination around: connected
  • Corpus frequency in the collocation scan: 6
  • Phrase length: 2 words
  • Average sentence length: 24.1 words

Words in this phrase

simply connected

Meanings of words in this phrase

  • simply can mean: In a simple way or state; considered in or by itself; without addition; alone. Common word
  • connected can mean: Having favorable rapport with a powerful entity. Frequent word

Sentence profile

  • Phrase position: 3 start, 7 middle, 6 end
  • Sentence types: 16 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

and even simply connected 1× any compact simply connected three dimensional 1× any two simply connected open subsets 1× indeed any simply connected polyhedron is 1× is a simply connected lie group 1× is not simply connected 1× of a simply connected bounded domain 1× of a simply connected lie group 1×

Sentence openings and endings

Common sentence openings:

as a corollary 1× as a first 1× completing the proof 1× for example the 1× however in order 1× in this case 1×

Common sentence endings:

a topological sphere 1× an equivalence relation 1× be simply connected 1× closed 3 manifold 1× connected lie groups 1× contain any holes 1×

Context words

These words often appear near this phrase in the example sentences:

group 7× lie 6× riemann 4× sphere 3× first 3× boundary 3× case 2× algebraic 2× spin 2× points 2× dimensional 2× theorem 2×

Related phrases

connected lie

Phrases around this combination

Just before it in the phrase index:

simple moving simple majority simple introduction simon property simon garfunkel simon fraser

Just after it in the phrase index:

simultaneous connections singapore airlines singer songwriter singh badal singh rajput singing competition

Corpus analysis

  • The phrase "simply connected" has 2 words and usually appears in the middle in these examples. The average sentence has 24.1 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as and even simply connected, any compact simply connected three dimensional, group, lie and riemann stand out.
  • In the phrase index, this combination connects with connected lie, linking the page to nearby combinations.

Example types with simply connected

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

The three-dimensional Euclidean space without the origin is connected, and even simply connected. (14 words)

Simply connected domains with arbitrary boundaries were first treated by William Fogg Osgood (1900). (14 words)

Simply connected spaces are those that, in a certain sense, do not have "holes". (14 words)

Longer example sentences

As a corollary of the theorem, any two simply connected open subsets of the Riemann sphere which both lack at least two points of the sphere can be conformally mapped into each other (because conformal equivalence is an equivalence relation). (40 words)

The universal cover of any connected Lie group is a simply connected Lie group, and conversely any connected Lie group is a quotient of a simply connected Lie group by a discrete normal subgroup of the center. (37 words)

Once the existence of u has been established, the Cauchy–Riemann equations for the holomorphic function g allow us to find v (this argument depends on the assumption that U be simply connected). (33 words)

Example sentences (16)

The universal cover of any connected Lie group is a simply connected Lie group, and conversely any connected Lie group is a quotient of a simply connected Lie group by a discrete normal subgroup of the center.

In this case the algebraic group Spin p,q is simply connected as an algebraic group, even though its group of real valued points Spin p,q (R) is not simply connected.

However, they are connected by tiny structures, so that the whole represents a simply connected set.

The three-dimensional Euclidean space without the origin is connected, and even simply connected.

As a corollary of the theorem, any two simply connected open subsets of the Riemann sphere which both lack at least two points of the sphere can be conformally mapped into each other (because conformal equivalence is an equivalence relation).

As a first application, he proved the Weil conjecture on Tamagawa numbers for the large class of arbitrary simply connected Chevalley groups defined over the rational numbers.

Completing the proof, Perelman takes any compact, simply connected, three-dimensional manifold without boundary and starts to run the Ricci flow.

For example, the surface of a convex or indeed any simply connected polyhedron is a topological sphere.

Advertentie

However, in order to be valid, the Dirichlet principle needs certain hypotheses concerning the boundary of U which are not valid for simply connected domains in general.

Intuitively, the condition that U be simply connected means that U does not contain any “holes”.

Moreover, every homomorphism between Lie algebras lifts to a unique homomorphism between the corresponding simply connected Lie groups.

Once the existence of u has been established, the Cauchy–Riemann equations for the holomorphic function g allow us to find v (this argument depends on the assumption that U be simply connected).

Ricci flow with surgery main Hamilton's program for proving the Poincaré conjecture involves first putting a Riemannian metric on the unknown simply connected closed 3-manifold.

Simply connected domains with arbitrary boundaries were first treated by William Fogg Osgood (1900).

Simply connected spaces are those that, in a certain sense, do not have "holes".

Smooth Riemann mapping theorem In the case of a simply connected bounded domain with smooth boundary, the Riemann mapping function and all its derivatives extend by continuity to the closure of the domain.

Advertentie