Parameterized Statistical Compactness of Topological Spaces

Abstract

In this research, we present the notion of statistical compactness restricted up to order $\alpha$, where $\alpha \in (0,1]$. There exist statistically compact spaces that are not compact. So the parameter $\alpha$ became the measurement of non compactness. Additionally, we looked for the continued existence of order $\alpha$ statistical compactness under open continuous surjection and sub-space topology. A finite intersection-like characterization for $\alpha$ statistical compactness has also been established.

Keywords

• Countable compactness
• natural density
• finite intersection property.

Project Number

NA

References

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