In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

In this paper, we consider the simplest class of stratified spaces -- linearly embedded graphs. We present an algorithm that learns abstract structure graph and models specific embedding from a point cloud sampled it. use tools inspiration computational geometry, algebraic topology, topological data analysis prove correctness identified under assumptions on embedding. The is implemented in Juli...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

We present Loopix, a low-latency anonymous communication system that provides bi-directional ‘third-party’ sender and receiver anonymity and unobservability. Loopix leverages cover traffic and Poisson mixing—brief independent message delays—to provide anonymity and to achieve traffic analysis resistance against, including but not limited to, a global network adversary. Mixes and clients self-mo...

Abstract The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is very well behaved analogue differential in the context topological spaces, satisfying good properties such as existence resolutions singularities handlebody decompositions. In this paper we prove Tanaka’s conjecture that any Whitney admits canonical structure. We thus est...

which is part of a certain 2d Hamiltonian cohomological field theory [11]. Here we use this map to study the topology of ΩHam(M, ω) and its Hofer geometric properties via a kind of virtual Morse theory for the positive Hofer length functional, L : ΩHam(M, ω) → R . We also use Ψ to prove a kind of index theorem for some critical points of L . We apply this theory to get some concrete application...

Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

Let X be a hypergroup. In this paper, we define a locally convex topology β on L(X) such that (L(X), β) with the strong topology can be identified with a Banach subspace of L(X). We prove that if X has a Haar measure, then the dual to this subspace is LC(X) ∗∗ = cl{F ∈ L(X);F has compact carrier}. Moreover, we study the operators on L(X) and L 0 (X) which commute with translations and convoluti...