Research Article NearlySoftMengerSpaces TareqM.Al-shami 1 andLjubiˇ saD.R.Koˇ cinac 2 1 Department of Mathematics, Sana’a University, Sana’a, Yemen 2 University of Niˇ s, Faculty of Sciences and Mathematics, 18000 Niˇ s, Serbia CorrespondenceshouldbeaddressedtoLjubiˇ saD.R.Koˇ cinac;lkocinac@gmail.com Received 18 March 2020; Accepted 5 May 2020; Published 26 May 2020 AcademicEditor:AliJaballah Copyright©2020TareqM.Al-shamiandLjubiˇ saD.R.Koˇ cinac.isisanopenaccessarticledistributedundertheCreative CommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedthe originalworkisproperlycited. Inthispaper,wedefineaweaktypeofsoftMengerspaces,namely,nearlysoftMengerspaces.Wegivetheircompletedescription usingsofts-regularopencoversandprovethattheycoincidewithsoftMengerspacesintheclassofsoftregular ⋆ spaces.Also,we studytheroleofenrichedandsoftregularspacesinpreservingnearlysoftMengernessbetweensofttopologicalspacesandtheir parametrictopologicalspaces.Finally,weestablishsomepropertiesofnearlysoftMengerspaceswithrespecttohereditaryand topological properties and product spaces. 1.Introduction etheoryofselectionprinciplesisanareaofmathematics that studies the possibility of generating a mathematical objectofonekindfromasequenceofobjectsofthesameor differentkind.ebeginningsofthistheoryaregoingback to Borel, Hurewicz, Menger, Rothberger, and Sierpi´ nski. is theory is one of the important tools of numerous subareas of mathematics such as set theory and general topology, Ramsey theory, game theory, hyperspaces, func- tion spaces, uniform structures, cardinal invariants, and dimension theory. In1924,Menger[1]studiedselectionpropertyunderthe name Menger basis property and Hurewicz [2], in 1925, reformulated it in the present form. Menger’s property is strictly between σ -compactness and Lindel¨ ofness. e pa- pers [3, 4] carried out a systematic study of selection principles in topology and then research in this field ex- panded immensely and attracted many researchers (see surveypapers[5–7]andreferencestherein).Sometypesof selection principles (so-called weak selection principles) have been formulated by applying the interior and closure operators in the definition of a selection property (see [8–21])andtheothertypeshavebeenexploredbyreplacing sequences of open covers by sequences of covers by some generalizedopensets(see[22–24]).Inthispaper,weapply theideasfromselectionprinciplestheorytosofttopological spaces. In fact, we are focused on a weaker form of the classical Menger covering property in the soft topology settings. SoftsetswereestablishedbyMolotdsov[25],in1999,asa new technique to approach real-life problems which suffer vagueanduncertainties.Heinvestigatedmeritsofsoftsets compared with probability theory and fuzzy set theory. Manyapplicationsofsoftsetshavebeenrecentlygivenon the different areas such as decision-making problem, in- formation theory, computer sciences, engineering, and medicalsciences.In2011,ShabirandNaz[26]employedsoft setsthataredefinedoveraninitialuniversesetwithafixed setofparameterstointroducetheconceptofsofttopological space. en, researchers have studied several concepts of classicaltopologicalspacesthroughsofttopologicalspaces. Softcompactness[27]andsomeweakvariantsofit[28–32] havebeenestablishedandinvestigated.Oneofdivergences between soft topological spaces and classical topological spaces was discussed in [33]. is paper is organized as follows. Section 2 provides basicdefinitionsandresultswhichareusedinthispaper.In Section3,weestablishsomepropertiesofsoftsemiopenand soft s-regular open sets which will help us to prove some Hindawi Journal of Mathematics Volume 2020, Article ID 3807418, 9 pages https://doi.org/10.1155/2020/3807418