In this paper, we characterize local $T_{0}$ and $T_{1}$ quantale-valued gauge spaces, show how these concepts are related to each other and apply them to $mathcal{L}$-approach distance spaces and $mathcal{L}$-approach system spaces. Furthermore, we give the characterization of a closed point and $D$-connectedness in quantale-valued gauge spaces. Finally, we compare all these concepts to each o...

We consider a nonconvex and nonclosed higher order differential inclusion and we prove the arcwise connectedness of the solution set.

ofThe Transcendental Critique Revisited and Revised Dooyeweerd’s account of abstraction is examined and found to be faulty. He holds that abstract thinkingisolates aspects which must then be synthesized, whereas I argue that we cannot isolate any aspect from the othershowever so hard we try. But our very inability to isolate aspects is then turned into an alternative version of ...

In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

It is known that connectedness is one of the important notions in topology. In this paper, a new notion of connectedness is introduced in L-topological spaces, which is called PS-connectedness. It contains some nice properties. Especially, the famous K. Fan’s Theorem holds for PS-connectedness in L-topological spaces.

We use the Shokurov connectedness principle and the Corti inequality to prove the birational superrigidity of a nodal hypersurface in P 5 of degree 5. We assume that all varieties are projective, normal and defined over C.

A general method is given whereby m-connectedness correlation functions can be studied in the percolation problem. The method for m=1 involves calculating the kth power of the correlation function ⟨σ(x)σ(x′)⟩ for a randomly dilute Ising model at nonzero temperature and subsequently averaging over configurations. The final step is to take the limit k→0. This method is tested by reproducing the s...

The restricted edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This paper determines that the restricted edge-connectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As consequences, the super edge-connectedness of B(d, n) is obtained immediately.