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Article Citation - WoS: 14Citation - Scopus: 14On Relations Between Transportation Cost Spaces and l1<(Academic Press inc Elsevier Science, 2020) Ostrovska, Sofiya; Ostrovskii, Mikhail I.The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space M, under which the transportation cost space on M contains an isometric copy of l(1). The obtained condition is applied to answer the open questions asked by Cuth and Johanis (2017) concerning several specific metric spaces. (2) The description of the transportation cost space of a weighted finite graph G as the quotient l(1) (E(G))/Z(G), where E(G) is the edge set and Z(G) is the cycle space of G. (C) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Complementability of Isometric Copies of L1 in Transportation Cost Spaces(Academic Press inc Elsevier Science, 2024) Ostrovska, Sofiya; Ostrovskii, Mikhail I.This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space X is such that the transportation cost space on X contains an isometric copy of L1, then it contains a 1-complemented isometric copy of $1. (c) 2023 Elsevier Inc. All rights reserved.Article Universality and Non-Embeddability Into Banach Spaces of Subspaces of the Real Line With the Gromov-Hausdorff Distance(Springer-Verlag Italia Srl, 2025) Ostrovska, Sofiya; Ostrovskii, Mikhail I.The paper aims to prove two universality results which can be used to simplify some of the available proofs of non-embeddability results for the Gromov-Hausdorff metrics.