Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy-fermion semimetals are a prototype of strongly correlated systems and, given their ...

The 3-arc graph of a digraph D is defined to have vertices the arcs of D such that two arcs uv, xy are adjacent if and only if uv and xy are distinct arcs of D with v 6= x, y 6= u and u, x adjacent. We prove Hadwiger’s conjecture for 3-arc graphs.

Metrizable spaces are studied in which every closed set is an α-limit for some continuous map and point. It shown that this property enjoyed by space containing sufficiently many arcs (formalized the notion of a with enough arcs), though such need not be arcwise connected. Further it preserved topological sums, products images quotients. However, positive results do hold metrizable obtained tho...

In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equili...