It is shown that the category of non-Archimedean metric spaces with l-Lipschitz maps can be embedded as a coreflectlve non-bireflective subcategory in the category of fuzzy uniform spaces. Consequential characterizations of topological and unif’orm properties are derived.

This is an addendum to the paper “Deformation of L∞-Algebras” [9]. We explain in which way the deformation theory of L∞-algebras extends the deformation theory of singularities. We show that the construction of semi-universal deformations of L∞-algebras gives explicit formal semiuniversal deformations of isolated singularities. Introduction In this paper, we apply the following general idea for...

L. Kauffman introduced a graphical link invariant which is the normalized Jones polynomial [4][5]. It is well-known that the polynomial is derived from the fundamental representation of the quantum group Uq(sl2). Further, G. Kuperberg constructed a graphical link invariant associated with the fundamental representation of the quantum group Uq(sl3) [10]. H. Murakami, T. Ohtsuki and S. Yamada int...

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to e...

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to e...

The notion of vertex operator algebra ([B], [FHL], [FLM]) is the algebraic counterpart of the notion of what is now usually called “chiral algebra” in conformal field theory, and vertex operator algebra theory generalizes the theories of affine Lie algebras, the Virasoro algebra and representations (cf. [B], [DL], [FLM], [FZ]). It has been well known (cf. [FZ], [L1]) that the irreducible highes...

This article is concerned with Alexandroff L-topological spaces and L-co-topological spaces, where L is a commutative, unital quantale. On one hand, an example is given to show that there is a finite strong L-topological space that is not Alexandroff. On the other hand, it is proved that every finite strong L-co-topological space is Alexandroff and that the category of Alexandroff strong L-co-t...