On H-closed topological semigroups and semilattices. (English) Zbl 1164.06332
Summary: 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.
MSC:
06F30 | Ordered topological structures |
06A12 | Semilattices |
22A15 | Structure of topological semigroups |
22A26 | Topological semilattices, lattices and applications |
54H12 | Topological lattices, etc. (topological aspects) |