On Chains in <Emphasis Type="BoldItalic">H</Emphasis>-Closed Topological Pospaces |
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Authors: | Oleg Gutik Dušan Pagon Dušan Repovš |
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Institution: | 1.Department of Mechanics and Mathematics,Ivan Franko Lviv National University,Lviv,Ukraine;2.Institute of Mathematics, Physics and Mechanics,Ljubljana,Slovenia;3.Faculty of Natural and Physics,University of Ljubljana,Ljubljana,Slovenia |
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Abstract: | We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space (H-closed topological semilattice) under which L contains a maximal (minimal) element. We also give sufficient conditions for a linearly ordered topological partially ordered
space to be H-closed. We prove that a linearly ordered H-closed topological semilattice is an H-closed topological pospace and show that in general, this is not true. We construct an example of an H-closed topological pospace with a non-H-closed maximal chain and give sufficient conditions under which a maximal chain of an H-closed topological pospace is an H-closed topological pospace. |
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