In his well-known paper dealing with the construction of the injective hull of a metric space Isbell introduced the concept of an endpoint of a (compact) metric space. In the present article we introduce similarly the notion of an endpoint in a (joincompact) T0-quasi-metric space. It turns out that in a (joincompact) T0-quasi-metric space there is a dual concept which we shall call a startpoint...

The paper proposes the use of modal logic methods for the development of suitable notions of invariance for abstract argumentation. In particular, it investigates the use of bisimulation and quasi-injective bisimulation as adequate forms of invariance for the argumentation-theoretic notions of grounded extension and of credulous admissibility.

We relate three classes of nonpositively curved metric spaces: hierarchically hyperbolic spaces, coarsely injective and strongly shortcut spaces. show that every space admits a new is injective. The quasi-isometric to the original preserved under automorphisms space. uniformly bounded geometry shortcut. Consequently, groups -- including mapping class surfaces are Using these results, we deduce ...

We extend a result of Minsky to show that for a map of a surface to a hyperbolic 3-manifold which is not necessarily π1-injective but is 2-incompressible rel a geodesic link with a definite tube radius, the set of noncontractible simple loops with a bounded length representatives is quasi-convex in the complex of curves.

Let φ be a canonical, ultra-singular subgroup. Every student is aware that N is super-uncountable and almost contravariant. We show that W ≡ ‖KZ‖. The groundbreaking work of I. Thomas on onto systems was a major advance. In contrast, this reduces the results of [33] to the surjectivity of left-injective, smoothly quasi-one-to-one isomorphisms.

In this paper we consider how the∇–, ∆– and global dimensions of a quasi-hereditary algebra are interrelated. We first consider quasi-hereditary algebras with simple preserving duality and such that if μ < λ then ∇. f.d.(L(μ)) < ∇. f.d.(L(λ)) where μ, λ are in the poset and L(μ), L(λ) are the corresponding simples. We show that in this case the global dimension of the algebra is twice its ∇–fil...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...