On ∂−locally compact space

The aim of this paper is to introduce and give preliminary investigation of ∂−locally compact spaces. Locally compactness and ∂−locally compactness are independent of each other. Every locally compact Hausdorff space is ∂−locally compact. But the converse is not true even though it be Hausdorff. ∂−locally compactness is a topological property. ∂−locally compactness is not preserved by the product topology.