On (τ1, τ2)-Star-I Compact Spaces

This paper introduces the concept of the (τ₁, τ₂)-star-ℐ compact space in an ideal bispace, where an ideal bispace is a quadruple (X, τ₁, τ₂, ℐ), τ₁, τ₂ being topologies defined on the set X and I being an ideal defined on X. The structure of (τ₁, τ₂)-star-ℐ compactness has been compared with some nearer structures like (τ₁, τ₂)-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 (τ₁, τ₂)-star-I compactness are revealed. It has been shown that real-valued continuous functions defined on (τ₁, τ₂)-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 (τ₁, τ₂)-star compactness is established by means of co-dense ideals.