Exploring topological properties in partial metric spaces: compactness and paracompactness

Compactness and paracompactness have been explored within the framework of partial metric spaces. It has been demonstrated that while a partial metric space may not be paracompact, induced partial metric spaces are indeed paracompact. Additionally, it has been shown that the compactness of a partial metric space can be analyzed through the pairwise compactness of the bitopological space induced by that partial metric.