On a complete topological inverse polycyclic monoid
Copyright policy )On a complete topological inverse polycyclic monoid
We give sufficient conditions when a topological inverse $\lambda$-polycyclic monoid $P_{\lambda}$ is absolutely $H$-closed in the class of topological inverse semigroups. For every infinite cardinal $\lambda$ we construct the coarsest semigroup inverse topology $\tau_{mi}$ on $P_\lambda$ and give an example of a topological inverse monoid $S$ which contains the polycyclic monoid $P_2$ as a dense discrete subsemigroup.
bicyclic monoid, Group Theory (math.GR), minimal topology, Topological semilattices, lattices and applications, Extensions of spaces (compactifications, supercompactifications, completions, etc.), QA1-939, FOS: Mathematics, Structure of topological semigroups, ``\(P\)-minimal'' and ``\(P\)-closed'' spaces, 22A15, 22A26, 54A10, 54D25, 54D35, 54H11, inverse semigroup, bicyclic monoid, polycyclic monoid, free monoid, semigroup of matrix units, topological semigroup, topological inverse semigroup, minimal topology, inverse semigroup, Mathematics - General Topology, Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), polycyclic monoid, General Topology (math.GN), інверсна напівгрупа, біциклічний моноїд, поліциклічний, вільний моноїд, напівгрупа матричних одиниць, топологічна напівгрупа, топологічна інверсна напівгрупа, мінімальна топологія, topological inverse semigroup, topological semigroup, semigroup of matrix units, Mathematics - Group Theory, Mathematics, free monoid, Topological groups (topological aspects)
bicyclic monoid, Group Theory (math.GR), minimal topology, Topological semilattices, lattices and applications, Extensions of spaces (compactifications, supercompactifications, completions, etc.), QA1-939, FOS: Mathematics, Structure of topological semigroups, ``\(P\)-minimal'' and ``\(P\)-closed'' spaces, 22A15, 22A26, 54A10, 54D25, 54D35, 54H11, inverse semigroup, bicyclic monoid, polycyclic monoid, free monoid, semigroup of matrix units, topological semigroup, topological inverse semigroup, minimal topology, inverse semigroup, Mathematics - General Topology, Several topologies on one set (change of topology, comparison of topologies, lattices of topologies), polycyclic monoid, General Topology (math.GN), інверсна напівгрупа, біциклічний моноїд, поліциклічний, вільний моноїд, напівгрупа матричних одиниць, топологічна напівгрупа, топологічна інверсна напівгрупа, мінімальна топологія, topological inverse semigroup, topological semigroup, semigroup of matrix units, Mathematics - Group Theory, Mathematics, free monoid, Topological groups (topological aspects)
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