📄 Abstract
We introduce and study several new notions in the framework of (ω)topological spaces—sets equipped with a countably increasing sequence of topologies. Specifically, we introduce (ω)Lindel¨of spaces (every (ω)open cover has a countable subcover), strongly (ω)Lindel¨of spaces, (ω)σ-compact spaces, and (ω)metacompact spaces (every (ω)open cover has, for some n, a point-finite (Jn)open refinement). We also introduce the notion of (ω)continuity and use it to show that (ω)continuous surjective images of (ω)Lindel¨of spaces are (ω)Lindel¨of. A central result (Theorem 3.12) establishes that every strongly (ω)Lindel¨of space that is (Jn)regular for each n ∈ N is (ω)paracompact, the (ω)topological analogue of the classical theorem that a regular Lindel¨of space is paracompact. We further prove that the product of an (ω)Lindel¨of space with an (ω)compact space is (ω)Lindel¨of, and that a space which is simultaneously (ω)Lindel¨of, (ω)metacompact and (Jn)normal for each n∈N is countably (ω)paracompact. Hereditary properties are also examined. 2010 Mathematics Subject Classification: 54A10.
🏷️ Keywords
📚 How to Cite:
R. Tiwari , ON (ω)LINDEL¨OF AND (ω)METACOMPACT TOPOLOGICAL SPACES , Volume 12 , Issue 6, June 2026, EPRA International Journal of Multidisciplinary Research (IJMR) , Pages: 289 - 294 , DOI: https://doi.org/10.36713/epra30441