In this paper, a certain new connectedness of L-fuzzy subsets inL-topological spaces is introduced and studied by means of preclosed sets. Itpreserves some fundamental properties of connected set in general topology.Especially the famous K. Fan’s Theorem holds.

We develop a general model of edge spaces in order to generalize, unify, and simplify previous work on cycle spaces of infinite graphs. We give simple topological criteria to show that the fundamental cycles of a (generalization of a) spanning tree generate the cycle space in a connected, compact, weakly Hausdorff edge space. Furthermore, in such a space, the orthogonal complement of the bond s...

In this article, we define the vector valued multiple of $chi^{2}$ over $p$-metric sequence spaces defined by Musielak and study some of their topological properties and some inclusion results.

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

there are dierent ways to code the geodesic flows on surfaces with negative curvature. such code spaces give a useful tool to verify the dynamical properties of geodesic flows. here we consider special subspaces of geodesic flows on hecke surface whose arithmetic codings varies on a set with innite alphabet. then we will compare the topological complexity of them by computing their topologica...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

Introduction § 0. Preliminaries: fuzzy sets 125 § 1. Fuzzy topological spaces: the basic categories of fuzzy topology 127 § 2. Fundamental interrelations between the category Top of topological 135 spaces and the categories of fuzzy topology § 3. Local structure of fuzzy topological spaces 138 § 4. Convergence structures in fuzzy spaces 140 § 5. Separation in fuzzy spaces 143 § 6. Normality and...

In this paper, we aim to develop a suitable homotopy theory of finite topological graphs by Khalimsky arcs. The notions developed are considered for the investigation of the algebraic invariants of topological graphs for their topological and graphical classifications. Keywords—Connected ordered topological spaces, digital topology, homotopy, Khalimsky spaces, topological graphs.

We present some results concerning definability of classes of topological spaces in hybrid languages. We use language Lt described in [9] to establish notion of “elementarity” for classes of topological spaces. We use it to prove the analogue of Goldblatt-Thomason theorem in topological spaces for hybrid languages H(E) and H(@). We also prove a theorem that allows to reformulate definability re...