A relation extends another relation consistently if its symmetric, respectively its asymmetric, part contains the corresponding part of the smaller relation. It is shown that there exists no finite circular chain made from two transitive relations A and B with at least one link from their asymmetric parts if and only if there exists a total preorder which consistently extends both. Additionally, this extension is uniquely determined if and only if the reflexive transitive closure of the union… Expand

In the beginning of this article we define the choice function of a non-empty set family that does not contain ∅ as introduced in [5, pages 88–89]. We define order of a set as a relation being… Expand

Preface In the notion of a topological vector space, there is a very nice interplay between the algebraic structure of a vector space and a topology on the space, basically so that the vector space… Expand