In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

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.

Topological entropy can be an indicator of complicated (chaotic) behavior in dynamical systems. Whether the topological entropy of a dynamical system is positive or not is of primary significance, due to the fact that positive topological entropy implies that one can assert that the system is chaotic. As the concept of topological entropy is concerned, it is hard, as remarked by [8], to get a g...

In the Iterated Immediate Snapshot model (IIS ) the memory consists of a sequence of one-shot Immediate Snapshot (IS ) objects. Each IS object can be accessed with an operation that atomically writes a value and returns a snapshot of its contents. Each process can access each IS object at most once. Processes access the sequence of IS objects, one-by-one, asynchronously, in a wait-free manner; ...

We introduce a functor which associates to every measure preserving system (X,B, μ, T ) a topological system (C2(μ), T̃ ) defined on the space of 2-fold couplings of μ, called the topological lens of T . We show that often the topological lens “magnifies” the basic measure dynamical properties of T in terms of the corresponding topological properties of T̃ . Some of our main results are as follow...

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...

The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the fam...