论文标题
在semigroup $ \ boldsymbol {b}_Ω^{\ mathscr {f} _n} $上，该_n} $由the the the the the $ \ mathscr {f} _n $的有限限制间隔的$ω$生成
On the semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$ which is generated by the family $\mathscr{F}_n$ of finite bounded intervals of $ω$
论文作者
论文摘要
我们研究了semigroup $ \ boldsymbol {b}_Ω^{\ mathscr {f}} $，该}是在论文[o中引入的。 Gutik和M. Mykhalenych，\ emph {关于Bicyclic Monoid的某些概括}，Visnyk lviv。大学。 ser。 Mech.-Mat。 \ textbf {90}（2020），5--19（在乌克兰人）]，如果nese $ \ mathscr {f} _n $由set $ \ {0,1，\ ldots，n \} $生成的情况。我们表明，绿色关系$ \ mathscr {d} $和$ \ Mathscr {J} $在$ \ boldsymbol {b}_Ω^{\ mathscr {\ mathscr {f} _N} $，半goloup $ \ boldsymbol {b boldsymbol {b} b}_Ω semigroup $ \ mathscr {i}_Ω^{n+1}（\ oftrightArrow {\ mathrm {cons}}} $的部分凸订单订单同构的$（ω，\ leqslant）$ rank $ \ leqslant n+1 $和leqslant）$ $ \ boldsymbol {b}_Ω^{\ mathscr {f} _n} $仅接受REES的一致性。另外，我们在Semigroup $ \ BoldSymbol {B}_Ω^{\ Mathscr {f} _n} $上研究了换档拓扑。特别是我们证明，对于任何转移$ t_1 $ -topology $τ$ in semogroup $ \ boldsymbol {b}_Ω^{\ Mathscr {f} $（\ boldsymbol {b}_Ω^{\ mathscr {f} _n}，τ）$，$ \ boldsymbol {b}_Ω^{\ Mathscr {f} $ω_ {\ mathfrak {d}} $ - 紧凑型换档$ t_1 $ - t_1 $ - topogy是紧凑的。我们描述了semigroup $ \ boldsymbol {b}_Ω^{\ mathscr {f} _n} $在Hausdorff Semitopological Semigroup中的关闭，并在拓扑相反的半元素$ \ boldsymbol {b boldsymbol {b}_Ω Hausdorff拓扑半群。
We study the semigroup $\boldsymbol{B}_ω^{\mathscr{F}}$, which is introduced in the paper [O. Gutik and M. Mykhalenych, \emph{On some generalization of the bicyclic monoid}, Visnyk Lviv. Univ. Ser. Mech.-Mat. \textbf{90} (2020), 5--19 (in Ukrainian)], in the case when the family $\mathscr{F}_n$ generated by the set $\{0,1,\ldots,n\}$. We show that the Green relations $\mathscr{D}$ and $\mathscr{J}$ coincide in $\boldsymbol{B}_ω^{\mathscr{F}_n}$, the semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$ is isomorphic to the semigroup $\mathscr{I}_ω^{n+1}(\overrightarrow{\mathrm{conv}})$ of partial convex order isomorphisms of $(ω,\leqslant)$ of the rank $\leqslant n+1$, and $\boldsymbol{B}_ω^{\mathscr{F}_n}$ admits only Rees congruences. Also, we study shift-continuous topologies on the semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$. In particular we prove that for any shift-continuous $T_1$-topology $τ$ on the semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$ every non-zero element of $\boldsymbol{B}_ω^{\mathscr{F}_n}$ is an isolated point of $(\boldsymbol{B}_ω^{\mathscr{F}_n},τ)$, $\boldsymbol{B}_ω^{\mathscr{F}_n}$ admits the unique compact shift-continuous $T_1$-topology, and every $ω_{\mathfrak{d}}$-compact shift-continuous $T_1$-topology is compact. We describe the closure of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$ in a Hausdorff semitopological semigroup and prove the criterium when a topological inverse semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$ is $H$-closed in the class of Hausdorff topological semigroups.
