Pseudogroups of transformations on discrete topological spaces

In all the earlier papers pseudogroups of transformations, generalised inverse semigroups and their connections were considered. This paper is a kind of recapitulation of these problems. Considering pseudogroups of transformations on discrete topological spaces is a step in the same direction. In this paper we notice that domains of functions belonging to a pseudogroup of transformations on discrete topological spaces - when we join an empty set to them create not only a topological space but also σ-body. We also consider pseudogroups on discrete topological spaces with the finite number of elements. The third problem is the influence of topology on relation of partial order.

---

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.