Abstract We prove that the homotopic distance between two maps defined on a manifold is bounded above by sum of their subspace distances critical submanifolds any Morse–Bott function. This generalizes Lusternik–Schnirelmann theorem (for Morse functions) and similar result Farber for topological complexity. Analogously, we that, analytic manifolds, submanifold its cut locus. As an application, s...

The causal and metric structure of globally hyperbolic spacetimes is investigated from a C∗-algebra point of view related to part of Connes’ noncommutative geometry programme. No foliation of the spacetime by means of spacelike surfaces is employed, but the complete Lorentzian geometry is considered. Several results are produced. As a first result, Connes’ functional formula of the distance is ...

Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.

In this paper, we prove some fixed point theorems for generalized multivalued mappings by using the c-distance recently introduced by Cho, Saadati and Wang [Y.J. Cho, R. Saadati and S.H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011), 1254-1260]. Our results improve and generalize the correspond ones of Ćirić [6], Feng and ...