فهرست نشریات علمی دسترسی آزاد ایران

The $T_D$ axiom, a low order separation axiom between $T_0$ and $T_1$, has been of interest to classical topologists for some time; latterly it has also proved interesting to pointfree topologists. Here we investigate it in the context of partial spaces and partial frames (think: $\sigma$-frames, $\kappa$-frames, frames, bounded distributive lattices). We establish an adjunction between the category of $T_D$ partial spaces with continuous maps and the category of partial frames with $D$-homomorphisms.    Several standard tools (covered primes, right adjoints, point closures) are not appropriate in our setting; we use linked pairs and slicing points instead. Of particular interest are the slicing points of free frames and congruence frames.We examine the fixed objects of the adjunction; both similarities and differences to the classical situation become clear. In particular, there are compact Hausdorff partial spaces that are not $T_D$. We introduce sharp partial frames, those for which all points are slicing and characterize these as well as the $T_D$ spatial and strongly $T_D$ spatial partial frames. We conclude with a comparison of sober and $T_D$ partial spaces.