in this paper, the concept of {sl local base with  stratifiedstructure} in $i$-topological vector spaces is introduced. weprove that every $i$-topological vector space has a balanced localbase with stratified structure. furthermore, a newcharacterization of $i$-topological vector spaces by means of thelocal base with stratified structure is given.

Background: The most important strategy of the immune system against pathogens is producing active oxygen intermediates with sidelong consequence of oxidative stress induction in body. Probiotics and selenium have recently been proven to be powerful antioxidants that help boost the immune system. Hence, the aim of this study was to investigate the antioxidant effects of Sac...

if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Protein-protein interaction (PPI) network analysis is a powerful strategy to understand M. tuberculosis (Mtb) system level physiology in the identification of hub proteins. In the present study, the PPI network of 79 Mtb toxin-antitoxin (TA) systems comprising of 167 nodes and 234 edges was investigated. The topological properties of PPI network were examined by 'Network analyzer' a cytoscape p...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...

Topologically ordered phases of matter, in particular so-called symmetry enriched topological (SET) phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z2 topologically ordered states in two dimensions, fundamental translations Tx and Ty acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a...

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...