Euler's Favorite Proof Meets a Theorem of Vantieghem

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...

My Favorite Theorem: Characterizations of Perfect Graphs

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

A new proof for the Banach-Zarecki theorem: A light on integrability and continuity

To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Proof General Meets Isawin

We describe the design and plan for implementing a combination of theorem prover interface technologies. On one side, we take from Proof General the idea of a prover-independent interaction language and its proposed implementation within the PG Kit middleware architecture. On the other side, we take from IsaWin a sophisticated desktop metaphor using direct manipulation for developing proofs. We...