Geodesic
On $H$-closed topological semigroups and semilattices
Algebra and discrete mathematics, no. 1 (2007), pp. 13-23

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In this paper, we show that if $S$ is an $H$-closed topological semigroup and $e$ is an idempotent of $S$, then $eSe$ is an $H$-closed topological semigroup. We give sufficient conditions on a linearly ordered topological semilattice to be $H$-closed. Also we prove that any $H$-closed locally compact topological semilattice and any $H$-closed topological weakly $U$-semilattice contain minimal idempotents. An example of a countably compact topological semilattice whose topological space is $H$-closed is constructed.
Keywords: Topological semigroup, $H$-closed topological semigroup, absolutely $H$-closed topological semigroup, topological semilattice, linearly ordered semilattice, $H$-closed topological semilattice, absolutely $H$-closed topological semilattice. 
@article{ADM_2007_1_a1,
     author = {Ivan Chuchman and Oleg Gutik},
     title = {On $H$-closed topological semigroups and semilattices},
     journal = {Algebra and discrete mathematics},
     pages = {13--23},
     publisher = {mathdoc},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_1_a1/}
}
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Ivan Chuchman; Oleg Gutik. On $H$-closed topological semigroups and semilattices. Algebra and discrete mathematics, no. 1 (2007), pp. 13-23. http://geodesic.mathdoc.fr/item/ADM_2007_1_a1/