A Straightforward Proof of De Gua’s Theorem

Another proof of Banaschewski's surjection theorem

We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...

Corrected proof of de Buda's theorem

< 6 I d m-d m l2 a*s. [5] V.V. Prelov, " Asymptotic behavior of the capacity of a continuous channel with a large amount of noise, " Probl. [ll] A.J. Viterbi, " Very low rate convolutional codes for maximum theoretical performance of spread-spectrum multiple-access channels " , IEEE J.

A simple proof of Renner’s exponential de Finetti theorem

In quantum information theory a de Finetti theorem expresses the fact that a quantum state ρ ∈ (Cd)⊗n that is invariant under permutation of its n subsystems is close to a mixture of tensor product states. The first such result is due to de Finetti [3], who showed that any classical distribution that is infinitely exchangeable can be expressed as a convex combination of product distributions. M...

A qui k proof of Sprindzhuk's de omposition theorem

Proof of Theorem A

Since the full proof of this theorem 10] is simple yet quite tedious, we connne ourselves to the guidelines of the proof. Observing the angles between the three sample points s i ; s j ; s k forming the minimal angle and the corresponding VD vertex v, we take advantage of the fact that d(v; s i) < d(s i ; s k) (Theorem 4.2(ii)) and, by trigonometric arguments, show that sin sin(120) R M