Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/2511 2023 2023 Mustansiriah University, Department of Mathematics, Iraq Murhaf Obaidi In this work, we study p-Lindelöf spaces, a concept which is "stronger" than Lindelöf spaces. Every p-compact space is proven to be p-Lindelöf space, so the concept of p-Lindelöf is a generalization of the concept of p-compact. Most of the theorems which are valid for p-compact spaces will be also valid for p-Lindelöf spaces, (with a slight modification). We also study local p-Lindelöf spaces with many related theorems and examples. 2023 2023 43 46 10.54216/PMTCS.020205 https://www.americaspg.com/articleinfo/40/show/2511