Lifted Takahashi Convexity on the Isbell-Convex Hull of an Asymmetrically Normed Real Vector Space

2026/03/12 by Philani Rodney Majozi, Mcedisi Sphiwe Zweni · 1 voice
Mathematics · #math.GN #math.FA

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arxiv published 2026/03/12 · arxiv updated 2026/05/23

Abstract

Künzi and Yildiz introduced convexity structures in the sense of Takahashi for T₀-quasi-metric spaces. In this article, we continue this line of study on the Isbell-convex hull of an asymmetrically normed real vector space. Using the canonical hull quasi-metric and the vector-space operations on E(X,‖⋅‖), we define a lifted convexity structure \mathbb W(f,g,λ)=λf⊕(1-λ)g and show that (E(X,‖⋅‖),q_E,\mathbb W) is a convex T₀-quasi-metric space. We further prove compatibility with the canonical embedding and relate the construction to W-convexity of minimal function pairs.

Citations

• A convexity of functions on convex metric spaces of Takahashi and\n applications
• Tight spans, Isbell completions and semi-tropical modules
• Injective hulls of certain discrete metric spaces and groups
• Tropical Convexity
• Six theorems about injective metric spaces
• Extension of uniformly continuous transformations and hyperconvex metric spaces

Discussions

• Philani Rodney Majozi, Mcedisi Sphiwe Zweni: A Takahashi convexity structure on the Isbell-convex hull of an asymmetrically normed real vector space https://arxiv.org/abs/2603.12101 https://arxiv.org/ [bsky, 0 points, 0 comments]

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