@article{Xu_Shi_2017, title={SPN-compactness in L-topological spaces}, volume={25}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1549}, DOI={10.4067/S0716-09172006000100004}, abstractNote={<span class="fontstyle0">In this paper, the notions of SPN-compactness, countable SPNcompactness and the SPN-Lindelöf property are introduced in </span><span class="fontstyle2">L</span><span class="fontstyle0">-topological spaces by means of strongly preclosed </span><span class="fontstyle2">L</span><span class="fontstyle0">-sets. In an </span><span class="fontstyle2">L</span><span class="fontstyle0">-space, an </span><span class="fontstyle2">L</span><span class="fontstyle0">set having the SPN-Lindelöf property is SPN-compact if and only if it is countably SPN-compact. (Countable) SPN-compactness implies (countable) N-compactness, the SPN-Lindelöf property implies the N-Lindelöf property, but each inverse is not true. Every </span><span class="fontstyle2">L</span><span class="fontstyle0">-set with finite support is SPN-compact. The intersection of an (a countable) SPN-compact </span><span class="fontstyle2">L</span><span class="fontstyle0">-set and a strongly preclosed </span><span class="fontstyle2">L</span><span class="fontstyle0">-set is (countably) SPNcompact. The strong preirresolute image of an (a countable) SPNcompact </span><span class="fontstyle2">L</span><span class="fontstyle0">-set is (countably) SPN-compact. Moreover SPN-compactness can be characterized by nets.</span>}, number={1}, journal={Proyecciones (Antofagasta, On line)}, author={Xu, Zhen-Guo and Shi, Fu-Gui}, year={2017}, month={May}, pages={47-61} }