Research On The Star-C-Menger Space And L-starcompact Space

Since van Douwen-Reed-Roscoe-Tree’s paper Star Covering Prop-erties was published, many other authors have studied star covering properties. In1996, M. Scheepers introduced the concept of selection principle to study the covering properties of topological spaces. In1999, Lj.D.R. Kocinac introduced star covering principles by intro-ducing star to selection principles. In this paper, we define the star-C-Menger spaces and study the relationship between star-C-Menger spaces and related spaces. We also study the properties of star-C-Menger spaces. At last, we study L-starcompact spaces. More pre-cisely,In Chapter1, we introduce the background of star-C-Menger spaces. At the same time, we introduce some symbols and preliminaries which are used in this paper.In Chapter2, first, we introduce the definition of star-C-Menger spaces and study the relationship between star-C-Menger spaces and related spaces. Then, we study the properties of star-C-Menger spaces, such as hereditarily and multiplicativity.In Chapter3, we give two counterexamples to show the relation-ship of L-starcompactness, star countable property and star-Lindelof property in pseudocompact spaces.