More on Rothberger Type Covering Properties and Novel Concepts for the Star-Menger Type Covering Properties in Bitopological Spaces

Abstract

In this paper, we investigate some weaker forms of the Rothberger covering property in a bitopological setting. We investigate the relationships between the bitopological weakly Rothberger, bitopological almost Rothberger and the Rothberger covering property in classical topological spaces. We also consider them under certain type of mappings, subspaces and products. Later, we introduce new types of the star-Menger covering property in bitopological spaces. By giving counter-examples, we see that our new forms are different from some of the existing covering properties. We establish conditions for their equivalences and pose some of the related covering properties for future research.

Keywords

• star-Lindelöf spaces
• bitopological spaces
• covering properties
• selection principles
• star-Menger spaces

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