On feebly compact semitopological semilattice $\exp_n\lambda$

TL;DR

This paper investigates feebly compact shift-continuous topologies on a specific semilattice, establishing conditions under which such topologies are sequentially pracompact and characterizing their compactness properties.

Contribution

It provides a characterization of feebly compact shift-continuous topologies on (\u03bb, ext{cap}) and links sequential pracompactness to (, ext{D}())-compactness.

Findings

Feebly compact shift-continuous topologies are sequentially pracompact iff they are (, ext{D}())-compact.

Characterization of _1-topologies on (, ext{cap}) with respect to compactness.

Conditions under which feebly compact topologies are sequentially pracompact.

Abstract

We study feebly compact shift-continous topologies on the semilattice $\left(\exp_n\lambda,\cap\right)$. It is proved that such $T_1$-topology is sequentially pracompact if and only if it is $\mathfrak{D}(\omega)$-compact.