Metric Spaces, Convexity and Nonpositive Curvature

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On Asymmetric Distances (2013, background): “9 in [17]; the proof is simply based on Prop.”
Firmly nonexpansive mappings in classes of geodesic spaces (2012, background): “We refer to [38] for an extensive study.”
The magnitude of metric spaces (2010, background): “A metric space A is geodesic [28] if for all a, b ∈ A there exists an isometry γ : [0, d(a, b)]→ A with γ(0) = a and γ(d(a, b)) = b.”
Morse Boundaries of Proper Geodesic Metric Spaces (2015, methodology): “βis identically bounded. It now follows from Lemma 2.5 (1) in [3] that βis a N′-Morse ray where N′ depends only on N and d(p,p′). To see the parameterized distance bound, we use Proposition 10.1.4 in [21]. To show the the Morse boundary is a quasi-isometry invariant, we show that under a quasi-isome”
Convex geodesic bicombings and hyperbolicity (2014, background): “Basic examples of convex geodesic bicombings are given by the linear geodesics σxy(t) := (1− t)x+ ty in a linearly convex subset X of a normed space or by the unique geodesics σxy : [0, 1] → X in a CAT(0) space [2, 4] or a Busemann space [1, 20] (where t 7→ d(σ(t), τ(t)) is convex for every pair of ”