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The goal of this work is to introduce and study two new types of ordered soft separation axioms, namely soft  T i  -ordered and strong soft  T i  -ordered spaces ( i  = 0, 1, 2, 3, 4). These two types are formulated with respect to the ordinary points and the distinction between them is attributed to the nature of the monotone neighborhoods. We provide several examples to elucidate the relationships among these concepts and to show the relationships associate them with their parametric topological ordered spaces and p-soft  T i  -ordered spaces. Some open problems on the relationships between strong soft  T i  -ordered and soft  T i  -ordered spaces ( i  = 2, 3, 4) are posed. Also, we prove some significant results which associate both types of the introduced ordered axioms with some notions such as finite product soft spaces, soft topological and soft hereditary properties. Furthermore, we describe the shape of increasing (decreasing) soft closed and open subsets of soft regularly ordered spaces; and demonstrate that a condition of strong soft regularly ordered is sufficient for the equivalence between p-soft  T  1 -ordered and strong soft  T  1 -ordered spaces. Finally, we establish a number of findings that associate soft compactness with some ordered soft separation axioms initiated in this work.

Two new forms of ordered soft separation axioms