Non-Hermitian topological phases bear a number of exotic properties, such as the non-Hermitian skin effect and breakdown conventional bulk-boundary correspondence. In this Letter, we introduce an unsupervised machine learning approach to classify based on diffusion maps, which are widely used in manifold learning. We find that will pose notable obstacle, rendering straightforward extension appr...

Non-Hermitian topological corner modes can be formed in exciton-polariton lattices under nonresonant pumping. Signals propagating the bulk of system travel around defects, which is not possible one-dimensional or two-dimensional with Hermitian edge states. In presence nonlinear interactions, remains topological, as evidenced by winding complex fluctuation spectrum. Finally, all polariton states...

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.

In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local bonding enforces constraints on low energy states which organize themselves into topologically distinct classes that break ergodicity but not any apparent symm...

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The en...

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...