Some properties of the Hausdorff tvs-cone pseudo-metric spaces

Let (X,d) be a tvs-cone metric space and let F0(X)={F:F is a nonempty closedsubset of X} endowed the Hausdorff tvs-cone pseudo-metric δ. This paper investigates some properties (including completeness, compactness, denseness, connectivity, etc) of (F0(X),δ) and establishes some relationships for these properties between (F0(X),δ) and (X,d). Results of this paper will be help to further deepen and richen superspaces theory from Hausdorff pseudo-metric spaces to Hausdorff tvs-cone pseudo-metric spaces.