On ( τ ₁ , τ ₂ )-Star-I Compact Spaces

This paper introduces the concept of the ( τ 1 , τ 2 )-star-ℐ compact space in an ideal bispace, where an ideal bispace is a quadruple ( X, τ 1 , τ 2 , ℐ), τ 1 , τ 2 being topologies defined on the set X and I being an ideal defined on X . The structure of ( τ 1 , τ 2 )-star-ℐ compactness has been compared with some nearer structures like ( τ 1 , τ 2 )- I compactness, strongly star- I compactness, countably I compactness, etc. With some counter examples, the distinct structures of these topological features have been validated. The nature of subspaces and the nature of functions that preserve the ( τ 1 , τ 2 )-star- I compactness are revealed. It has been shown that real-valued continuous functions defined on ( τ 1 , τ 2 )-star- I fin compact spaces are bounded. A characterization of this specific topological property in terms of a finite intersection property is provided. Finally, the relation with weakly ( τ 1 , τ 2 )-star compactness is established by means of co-dense ideals.