On feebly compact shift-continuous topologies on the semilattice ${\exp }_n\lambda$

Abstract

We study feebly compact topologies $\tau$ on the semilattice $\left({\exp }_n\lambda ,\cap \right)$ such that $\left({\exp }_n\lambda ,\tau \right)$ is a semitopological semilattice and prove that for any shift-continuous $T_1$-topology $\tau$ on ${\exp }_n\lambda$ the following conditions are equivalent: $(i)$~$\tau$ is countably pracompact; $(ii)$ $\tau$ is feebly compact; $(iii)$ $\tau$ is $d$-feebly compact; $(iv)$ $\left({\exp }_n\lambda ,\tau \right)$ is an $H$-closed space.

arXiv comment7 pages. arXiv admin note: text overlap with arXiv:1606.00395