In last ten years many mathematicians have studied properties of BL-algebras endowed with a topology. For example A. Di Nola and L. Leustean cite{dn} studied compact representations of BL-algebras, L. C. Ciungu cite{ciu} investigated some concepts of convergence in the class of perfect BL-algebras, J. Mi Ko and Y. C. Kim cite{jun} studied relationships between closure operators and BL-algebras,...

This paper is an expanded version of the talk I gave at the rst ECM held in Paris in July 92. Quantum groups, or better quantized enveloping algebras have been deened around 1985 by Drinfeld and Jimbo, D], J], as neither commutative nor cocommutative Hopf algebras obtained by suitably deforming the deening relations of the enveloping algebra of a semisimple Lie algebra. This new theory has alre...

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

In the topos approach to quantum physics, a functor known as the spectral presheaf of a von Neumann algebra plays the role of a generalized state space. Mathematically, the spectral presheaf also provides an interesting generalization of the Gelfand spectrum, which is only defined for abelian von Neumann algebras, to the nonabelian case. A partial duality result, analogous to Gelfand duality, e...

The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the Mizar Mathematical Library, there are some attempts to formalize prime ideals and filters; one series of articles written as decoding [9] proven some results; we tried however to follow [21], [12], and [13]. All three were devoted to the Stone repr...