jordan curve sentence in Hindi
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- The statement of the Jordan curve theorem may seem obvious at first, but it is a rather difficult theorem to prove.
- Replacing ? by a homotopic curve, it may be assumed that ? is a smooth Jordan curve ? with non-vanishing derivative.
- Some examples are the Hahn Banach theorem, K�nig's lemma, Brouwer fixed point theorem, G�del's completeness theorem and Jordan curve theorem.
- The proof of the Jordan curve theorem for " differentiable curves " is not difficult, and can be done using mathematics available to Gauss.
- One proof of the impossibility of finding a planar embedding of " K " 3, 3 uses a case analysis involving the Jordan curve theorem.
- In fact, it's a simple corollary of the Jordan curve theorem ( which basically says every simple closed curve has an inside and outside ).
- :: : Smale is talking about the Jordan curve theorem, which states that a closed continuous curve in the plane has an inside and an outside.
- Completing the curve to a Jordan curve by adding part of the boundary of the smaller disk, the formula reduces to the planar Green-Stokes formula.
- The first formal proof of the Jordan curve theorem was created by in the HOL Light system, in January 2005, and contained about 60, 000 lines.
- He proved the Jordan curve theorem in 1905; while this was long considered the first rigorous proof, many now also consider Jordan's original proof rigorous.
- :: : In the 20th century, the Jordan curve theorem became a subject of intense study, because it was related to the formal axiomatization of topology.
- :When you talk about the topology of space you may get into some difficulties proving things that seem intuitively obvious; see Jordan Curve Theorem as an example.
- Since ? does not separate the surface, there is a smooth Jordan curve ? ( with non-vanishing derivative ) which cuts ? transversely at only one point.
- In particular, it is impossible to dissect a circle and make a square using pieces that could be cut with scissors ( that is, having Jordan curve boundary ).
- Applications of the fundamental groupoid on a set of base points to the Jordan curve theorem, covering spaces, and orbit spaces are given in Ronald Brown's book.
- In 1920, BronisBaw Knaster and Kazimierz Kuratowski asked whether a nondegenerate homogeneous continuum in the Euclidean plane "'R "'2 must be a Jordan curve.
- In fact suppose a region on the Riemann sphere is given by the exterior of " n " disjoint Jordan curves and that " is an exterior point.
- :: : But the proof of the Jordan curve theorem for " continuous curves " without assuming differentiability, is more subtle, because continuous curves can be complicated.
- Now combining C1 with C satisfies the requirements of the Jordan Curve Theorem and generates two connected components, E1 and E2, with C1 + C as the boundary between them.
- Due to the importance of the Jordan curve theorem in low-dimensional topology and complex analysis, it received much attention from prominent mathematicians of the first half of the 20th century.
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