On feebly compact shift-continuous topologies on the semilattice expnλ

Анотація

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