On ∂-partial-locally compact space

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