Basic theory of s-posets

Abstract

In this paper, we have established the notions of soft order relations and studied its basic structural properties. We give the concepts of soft maximum, soft minimum, soft maximal, soft minimal, soft infimum and soft supremum in any s-poset. Then, the concept of soft order preserving mapping is defined and given some basic results. Moreover, it has been shown that the topology derived from a soft partial order relation is a soft topology which will substitute as a soft version of Alexandroff topology in classical theory. With all that, we obtained the category SPOSET of s-posets, and constructed a functor which is called ostracizer functor between the categories SPOSET and POSET .