A note on nearly Alster spaces and its interrelations with some covering properties

Key Points

• This research aims to define a new Alster property and analyze its relations to other forms and covering properties.
• Introduction of a new Alster property.
• Investigating relationships with weaker forms of Alster spaces.
• Using counter-examples to differentiate nearly Alster properties.
• Analysis of productively nearly Lindelöf spaces.
• Characterization of nearly Alster property using selection principles.
• Identification of key differences between nearly Alster property and other properties.
• Insights into the topological characteristics of nearly Alster spaces.
• Clear definitions and understandings regarding selective covering properties.