In this paper the notion of fuzzy BF -algebra and fuzzy topological BF -algebras are introduced. We stated and proved some theorem in fuzzy BF -algebras and level subalgebras. Finally the Foster’s results on homomorphic images and inverse images in fuzzy topological BF algebras are studied. Mathematics Subject Classification: 06F35, 03G25, 94D05

For a simple Lie algebra g we define a system of linear ODEs with polynomial coefficients, which we call the topological equation of g-type. The dimension of the space of solutions regular at infinity is equal to the rank of the Lie algebra. For the simplest example g = sl2(C) the regular solution can be expressed via products of Airy functions and their derivatives; this matrix valued function...

If X is a topological space we denote by C(X) ® Mn the algebra of continuous functions from X to the algebra Mn of n x n complex matrices. A complete characterization of those topological spaces Y is given (in terms of vector bundles on Y) such that each unital algebrahomomorphism Φ: C(X) Θ Mn —• C(Y) Mkn is of the form a o (Φ' ® idΛ) for some homomorphism Φ': C(X) -+ C(Y) ® Λ/* and some su...

We investigate the Arens products on the biduals of certain algebras of operators on nonreflexive Banach spaces. To be precise, we study the α-nuclear operators, where α is a tensor norm. This includes the approximable and nuclear operators, and we use these, together with the 2-nuclear operators, as motivating examples. The structure of the two topological centres of the bidual are studied, an...

In this paper we propose and partially carry out a program to use K-theory to refine the topological realization problem of unstable algebras over the Steenrod algebra. In particular, we establish a suitable form of algebraic models for K-theory of spaces, called ψ-algebras, which give rise to unstable algebras by taking associated graded algebras mod p. The aforementioned problem is then split...

String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal’s definition of a conformal field theory. Relations with conformal field theory, topological field theory and topological gravity are studied. For each field theory, an algebraic counterpart, the (homotopy) algebra satisfied by the tree level correlators, is construc...

In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus giving the means to actually insert complex values for the deformation parameter. Moreover we establish a topological duality theory for locally convex Hopf alg...

We establish a general result about extending a right invertible row over a Banach algebra to an invertible matrix. This is applied to the computation of right topological stable rank of a split exact sequence. We also introduce a quantitative measure of stable rank. These results are applied to compute the right (left) topological stable rank for all nest algebras. This value is either 2 or in...

We describe algebraic obstruction theories for realizing an abstract (co)algebra K∗ over the mod p Steenrod algebra as the (co)homology of a topological space, and for distinguishing between the p-homotopy types of different realizations. The theories are expressed in terms of the Quillen cohomology of K∗.

For a locally compact Hausdorff semigroup S, the L representation algebra R(S) was extensively studied by Dunkl and Ramirez. The FourierStieltjes algebra F (S) of a topological semigroup was studied by Lau. The aim of this paper is to investigate these two algebras and study the amenability of them with respect to the structure of S.