BETA
Examples ofconnected sum
Dictionary> Examples ofconnected sum
connected sumisn’t in the Cambridge Dictionary yet. You can help!
Add a definition
A proof-structure is seen as aconnectedsumof tori with boundaries, the boundaries representing conclusions.
From theCambridge English Corpus
In particular, = 0 corresponds to the tree sum and = 1 to theconnectedsum.
From theCambridge English Corpus
Theconnectedsumat two or three of the three points where these horospheres are tangent produces an embedded genus-0, or genus-1, surface.
From theCambridge English Corpus
Indeed, one can consider theirconnectedsumat the three points where they are tangent and produce an embedded genus-1 surface with three ends.
From theCambridge English Corpus
The dependence ('interaction', 'entanglement') between occurrences of formulas in a sequent, which it is quite natural to understand as aconnectedsum.
From theCambridge English Corpus
Tensor and cotensor still correspond to disjoint union andconnectedsum.
From theCambridge English Corpus
Note that if or is not connected, theirconnectedsumis not unique; it depends on the choice of connected components, which are linked by the cylinder.
From theCambridge English Corpus
Every nonempty, compact, connected 2-manifold (or surface) is homeomorphic to the sphere, aconnectedsumof tori, or aconnectedsumof projective planes.
From
This example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Thus, such a sphere either does not separate the 3-manifold or gives a nontrivialconnectedsumdecomposition.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The resultingconnectedsumis the square knot.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.It can be obtained by attaching three handles to a sphere or by gluing (taking theconnectedsum) of three tori.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The third is the only example of a non-trivialconnectedsumwith a geometric structure.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.To produce a well-defined symplectic structure, theconnectedsummust be performed with special attention paid to the choices of various identifications.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.This is the simplest case of theconnectedsumof "n" tori.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.It is closely related to the square knot, which can also be described as aconnectedsumof two trefoils.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.To form theconnectedsumof more than two surfaces, sum two of them at a time until they are all connected.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Any knot can be uniquely expressed as aconnectedsumof prime knots.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.If both manifolds are oriented, there is a uniqueconnectedsumdefined by having the gluing map reverse orientation.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.So theconnectedsumof knots has a more elaborate definition that produces a well-defined embedding, as follows.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
- be-on-the-flat
- be on the go
- be-on-the-go
- be on the horns of a dilemma
- be-on-the-horns-of-a-dilemma
- be on the level
- be-on-the-level
- be on the line
- be-on-the-line
- be on the make
- be-on-the-make
- be on the mend
- be-on-the-mend
- be on the move
- be-on-the-move
- be-on-the-point-of
- be on the point of (doing) something
- be on the point of (doing) sth
- be-on-the-point-of-doing-sth
- be on the pull
- be-on-the-pull
- be on the rack
- be-on-the-rack
- be on the receiving end
- be-on-the-receiving-end