On Statistical Star-Compactness Restricted up to Order $\alpha$

Abstract

Expanding the concept of star compactness for a countable case, we confine the star statistical compactness up to order $\alpha$, and the value of $\alpha$ is between 0 and 1. We compare this idea with other topological aspects pertaining to star statistical compactness of order $\alpha$. This work illustrates the properties of this topological attribute and it's subspaces under various conditions, particularly under open continuous surjection. It is obtained that star statistical compactness of order $\alpha$ can be characterized by countable family of closed sets with some added set theoretic attributes.

Keywords

• asymptotic density
• compactness
• star operator

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