in this paper, the concept of countably near ps-compactness inl-topological spaces is introduced, where l is a completely distributive latticewith an order-reversing involution. countably near ps-compactness is definedfor arbitrary l-subsets and some of its fundamental properties are studied.

we obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. also weconsider relations kadec-klee property and shur property with this objects.these theorems are extend of papers mohebi and narayana.

In the context of optimal transport (OT) methods, subspace detour approach was recently proposed by Muzellec and Cuturi. It consists first finding an plan between measures projected on a wisely chosen then completing it in nearly whole space. The contribution this paper is to extend category methods Gromov–Wasserstein problem, which particular type OT distance involving specific geometry each d...

It is well known that, when endowed with the Gromov-Hausdorff distance dGH, collection M of all isometry classes compact metric spaces a complete and separable space. also that (M,dGH) geodesic space, but there no structural characterization geodesics in M. In this paper we provide two characterizations We call γ:[0,1]→M Hausdorff-realizable if exists space Z containing isometric copies γ(t) fo...