It is known that any MV -algebra is a topological MV -algebra. For a locally finite MV -algebra A with some algebraic and topological conditions the product A× A becomes a compact Riemann surface (modulo conformal equivalence). Topologically, it is a torus.

We prove that the topology of a compact Hausdorff topological Heyting algebra is a Stone topology. It then follows from known results that a Heyting algebra is profinite iff it admits a compact Hausdorff topology that makes it a compact Hausdorff topological Heyting algebra.

We characterize positive topological entropy for quasi-state space homeomorphisms induced from C∗-algebra automorphisms in terms of dynamically generated subspaces isomorphic to l1. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as ...

Motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by S. Vickers, providing an algebraic and a coalgebraic category of the new structures. As a result, the nature of the category   TopSys   of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...

We study the topologically twisted string theory on the general back-ground AdS3× N which is compatible with the world-sheet N = 2 superconformal symmetry and is extensively discussed in the recent works [20]. After summarizing the algebraic structure of the world-sheet topological theory, we show that the space-time (boundary) conformal theory should be also topological. We directly construct ...

Here, we define (semi)topological L-algebras and some related results are approved. Then deduce conditions that mention an L-algebra to be a semi-topological or topological check attributes of them. Chiefly, display in L, if (L, ↠, τ ) is {1} open set L bounded satisfies the double negation property, then (L,τ) L-algebra. Finally, construct discrete topology on quotient L-algebra, under suit- a...

This abstract is a summary of a lecture given at the Seminar of the Department of Logic and Methodology of Sciences, Wroc law University, 23 May 1985. The present work refers directly to the investigations of Buszkowski and Prucnal [1] and that of Esakia [2], generalizing their results. Our main representation theorem for co-diagonalizable algebras (Theorem 2) is obtained by application of cert...

Working within a complete not necessarily atomic Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalize complement on a lattice which in turn abstracts the set theoretic operator. Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors. We consider properties of such lattices and their interrelations. Ma...

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend open-closed two-dimensional topological field theories to nonorientable surfac...

We introduce the notion of a half-ribbon Hopf algebra, which is a Hopf algebra H along with a distinguished element t ∈ H such that (H, R,C) is a ribbon Hopf algebra, where R = (t ⊗ t)∆(t) and C = t. The element t is closely related to the topological ‘half-twist’, which twists a ribbon by 180 degrees. We construct a functor from a topological category of ribbons with half-twists to the categor...