Pre-Hausdorff and Hausdorff objects in the category of quantale-valued closure spaces

Abstract

In previous papers, several $T_{0}$ and Hausdorff objects in topological categories are introduced and compared. The main objectives of this paper are to characterize $\overline{T_{0}}$, $T_{0}$, $T_{1}$ and pre-$\overline{T_{2}}$ objects in the category of quantale-valued closure space as well as to examine their mutual relationship.

Keywords

• $\mathcal{V}$-closure space
• $\mathcal{V}$-topological space
• topological category
• separation
• Hausdorff objects

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