Lindelof spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindelof, weakly Lindelof, and quasi-Lindelof, that have been considered in various research papers. Here we present a comparison between the standard results on Lindelof spaces and analogous results for weakly and almost Lindelof spaces. Some theorems, similar to the published ones, will be proved. We also consider counterexamples, most of which have not been included in the standard Topological textbooks, that show the interrelations between those properties and various basic topological notions, such as separability, separation axioms, first countability, and others. Some new features of those examples will be noted in view of the present comparison. We also pose several open questions.

Author Bio

Petra Staynova is an undergraduate reading for a Master's in Mathematics and Philosophy at Pembroke College, Oxford University. Even while in High School, she was fascinated by 'rubber-sheet geometry', or Topology. She pursued this interest by taking the Topology courses in Oxford and (in her 3d year ) writing an 'Extended Essay' titled 'Lindelof-type Covering Properties of Topological Spaces and Separation Axioms'. The current article, "A Comparison of Lindelof-type Covering Properties in Topological Spaces", comprises a revised and shortened version of that essay. She has two other papers that appeared in the journal "Mathematics and Mathematical Education", published by the Bulgarian Mathematical Society. She has also given talks at the 39th and 40th Spring Conference of the Union of Bulgarian Mathematicians. Besides her interests in Mathematics, Petra is a published writer; her most recent essay, 㤼㸳Rock the Cradle of Democracy: Kavarna’s Sunrise" co-won the first prize of SEVEN Fund's 'New Models of Economic Development' competition (http://www.sevenfund.org/new-models-development/). Petra also enjoys Ballroom and Latin American dancing, as well as practicing T’ai Chi. Following graduation, she is planning on pursuing a PhD and a career in Mathematics.