jordan curve sentence in Hindi
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- :: If the closed Jordan curve ? separates the surface, it is homotopic to a smooth Jordan curve ? ( with non-vanishing derivative ) that separates the surface into two halves.
- :: If the closed Jordan curve ? separates the surface, it is homotopic to a smooth Jordan curve ? ( with non-vanishing derivative ) that separates the surface into two halves.
- Hence, for the definition of the functional calculus, indeed a suitable family of Jordan curves can be found for each " f " that is holomorphic on some " D ".
- Thus to check exactness of a closed form it suffices to show that the vanishing of the integral around any regular closed curve, i . e . a simple smooth Jordan curve with nowhere vanishing derivative.
- The Jordan curve theorem was independently generalized to higher dimensions by H . Lebesgue and L . E . J . Brouwer in 1911, resulting in the "'Jordan Brouwer separation theorem " '.
- Here A is the area of the region bounded by a closed Jordan curve of length ( perimeter ) L in the plane, R is the circumradius of the bounded region, and r is its inradius.
- So, roughly speaking, in the case of one function the image is a slit region in the complex plane; and in the case of two functions the two regions are separated by a closed Jordan curve.
- The previous discussion has shown that the integral makes sense, i . e . a suitable collection ? of Jordan curves does exist for each " f " and the integral does converge in the appropriate sense.
- A fundamental domain for the action of a Schottky group " G " on its regular points ? ( " G " ) in the Riemann sphere is given by the exterior of the Jordan curves defining it.
- Both the Mizar and the HOL Light proof rely on libraries of previously proved theorems, so these two sizes are not comparable . showed that the Jordan curve theorem is equivalent in proof-theoretic strength to the weak K�nig's lemma.
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