We study Borel measurability of the spectrum in topological algebras. We give some equivalences of the various properties, show that the spectrum in a Banach algebra is continuous on a dense Gs, and prove that in a Polish algebra the set of invertible elements is an FaS and the inverse mapping is a Borel function of the second class. This article has its origin in the papers [7] and [5]. We stu...

We give a very brief survey on ZFC theory (Zermelo-Fraenkel Set Theory) and we present an intuitive introduction to the method of forcing and some applications to the real line. Our exposition will be very informal, without any claim of completeness and rigour. The idea is just to give a very intuitive idea of what Set Theory and forcing-method are, and why they are interesting and useful from ...

We generalize Stochastic Mathematical Programs with Equilibrium Constraints (SMPEC) introduced by Patriksson and Wynter [Operations Research Letters, Vol. 25, pp. 159–167, 1999] to allow joint upper-level constraints, and to change continuity assumptions w.r.t. uncertainty parameter assumed before by measurability assumptions. For this problem, we prove the measurability of a lower-level mappin...