We study Kuperberg invariants for sutured manifolds in the case of a semidirect product an involutory Hopf superalgebra $H$ with its automorphism group $\text{Aut}(H)$. These are topological balanced 3-manifolds endowed homomorphism fundamental into $\text{Aut}(H)$ and possibly $\text{Spin}^c$ structure homology orientation. show that these computed via form Fox calculus that, if is $\mathbb{N}...

The edge-contraction axioms are introduced for topological recursion of multilinear maps that arise from cellular graphs, and it is proven that these axioms are equivalent to topological quantum field theories over a Frobenius algebra, assuming the consistency of the axioms. As an example, the concrete formulas of topological quantum field theories on the finite-dimensional abelian group algebr...

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.

The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, s...

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 ...

In this paper, some fundamental concepts are given relating to fuzzytopological spaces. Then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. Also the fuzzy topological spaces which are Hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

Systems of spatial data types and operations, or spatial algebras, are fundamental for the implementation of spatial database systems. Several designs of such algebras have been proposed in the last decade, and recently commercial DBMS ooer such algebras in the form of extension packages (e.g. data bladess). However, actual implementations are generally severely restricted when compared to desi...