Publication Date



Technical Report: UTEP-CS-14-56

Published in Mathematical Structures and Modeling, 2014, Vol. 31, pp. 18-26.


In many real life situations, a text consists of related parts; so, to understand a part, we need to first understand some (or all) preceding parts: e.g., to understand Chapter 3, we first need to understand Chapters 1 and 2. In many cases, this dependence is described by a partial order. For this case, O.~Prosorov proposed a natural description of the dependence structure as a topology (satisfying the separation axiom T0).

In some practical situations, dependence is more general than partial order: e.g., to understand Chapter 3, we may need to understand either Chapter 1 or Chapter 2, but it is not necessary to understand both. We show that such a general dependence can be naturally described by a known generalization of topology: the notion of an interior (or, equivalently, closure) structure (provided, of course, that this structure satisfies a natural analog of T0-separability).