In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP.

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...

We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dgand spectral categories. Our proof is mainly based on a fundamental property of cofibrant enriched categories on two objects, stated below as the Interval Cofibra...

The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and...

We consider Lifshitz criticalities with dynamical exponent z=2 z=2 that emerge in a class of topological chains. There, such criticality plays fundamental role describing transitions between symmetry-enriched conformal field theories (CFTs)...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct C(L), called the tower extension of C (indexed by L). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spac...

in this paper the concept of metacompactness in l-topologicalspaces is introduced by means of point finite families of l-fuzzy sets. thisfuzzy metacompactness is a natural generalization of lowen fuzzy compactness.further a characterization of fuzzy metacompactness in the weakly inducedl-topological spaces is also obtained.

A non-trivial example of an L-topological space, the L-fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.