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- ДокументA metrizable Lawson semitopological semilattice with non-closed partial order(2020) Taras Banakh, Serhii Bardyla, Alex RavskyWe construct a metrizable Lawson semitopological semilattice $X$ whose partial order $le_X,={(x,y)in Xtimes X:xy=x}$ is not closed in $Xtimes X$. This resolves a problem posed earlier by the authors.
- ДокументHeegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$(2020) Christian Hatamian, Alexandr PrishlyakThe present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies. It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$. Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described. Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories
- ДокументOpen finite-to-one functions on open topological graphs(2020) Ігор Юрійович ВласенкоThe paper describes homotopy classes of open continuous functions on finite open topological graphs